المؤلفون: Bardhan, Bijoya, Sen, Mausumi, Sharma, Debashish

مصطلحات موضوعية: keyword:inverse eigenvalue problem, keyword:unicyclic graph, keyword:leading principal submatrices, msc:05C50, msc:15A24, msc:65F18

وصف الملف: application/pdf

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الاتاحة: http://hdl.handle.net/10338.dmlcz/152316

المؤلفون: Ma, Yuzheng, Shao, Yanling

مصطلحات موضوعية: keyword:graph, keyword:generalized distance matrix, keyword:generalized distance eigenvalue, keyword:generalized distance spread, msc:05C12, msc:05C50, msc:15A18

وصف الملف: application/pdf

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الاتاحة: http://hdl.handle.net/10338.dmlcz/152263

المؤلفون: Bhamre, Vandana P., Pawar, Madhukar M.

مصطلحات موضوعية: keyword:covering energy of poset, keyword:eigenvalue, keyword:spectrum, keyword:upper bound, keyword:lower bound, msc:05B20, msc:05C50, msc:06A07, msc:06A11, msc:06B05, msc:06B99

وصف الملف: application/pdf

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الاتاحة: http://hdl.handle.net/10338.dmlcz/151973

المؤلفون: Milovanović, Emina, Bozkurt Altindağ, Serife B., Matejić, Marjan, Milovanović, Igor

مصطلحات موضوعية: keyword:Laplacian graph spectra, keyword:bipartite graph, keyword:spread of graph, msc:05C50, msc:15A18

وصف الملف: application/pdf

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الاتاحة: http://hdl.handle.net/10338.dmlcz/151670

المؤلفون: Ganie, Hilal A., Ul Shaban, Rezwan, Rather, Bilal A., Pirzada, Shariefuddin

مصطلحات موضوعية: keyword:distance matrix, keyword:energy, keyword:distance Laplacian matrix, keyword:distance Laplacian energy, msc:05C12, msc:05C50, msc:15A18

وصف الملف: application/pdf

Relation: mr:MR4586898; zbl:Zbl 07729511; reference:[1] Aouchiche, M., Hansen, P.: Two Laplacians for the distance matrix of a graph.Linear Algebra Appl. 439 (2013), 21-33. Zbl 1282.05086, MR 3045220, 10.1016/j.laa.2013.02.030; reference:[2] Aouchiche, M., Hansen, P.: Distance spectra of graphs: A survey.Linear Algebra Appl. 458 (2014), 301-386. Zbl 1295.05093, MR 3231823, 10.1016/j.laa.2014.06.010; reference:[3] Aouchiche, M., Hansen, P.: Some properties of the distance Laplacian eigenvalues of a graph.Czech. Math. J. 64 (2014), 751-761. Zbl 1349.05083, MR 3298557, 10.1007/s10587-014-0129-2; reference:[4] Brouwer, A. E., Haemers, W. H.: Spectra of graphs.Universitext. Berlin: Springer (2012). Zbl 1231.05001, MR 2882891, 10.1007/978-1-4614-1939-6; reference:[5] Cvetković, D. M., Doob, M., Sachs, H.: Spectra of Graphs: Theory and Application.Pure and Applied Mathematics 87. Academic Press, New York (1980). Zbl 0824.05046, MR 0572262; reference:[6] Das, K. C., Aouchiche, M., Hansen, P.: On (distance) Laplacian energy and (distance) signless Laplacian energy of graphs.Discrete Appl. Math. 243 (2018), 172-185. Zbl 1387.05147, MR 3804748, 10.1016/j.dam.2018.01.004; reference:[7] Díaz, R. C., Rojo, O.: Sharp upper bounds on the distance energies of a graph.Linear Algebra Appl. 545 (2018), 55-75. Zbl 1390.05124, MR 3769113, 10.1016/j.laa.2018.01.032; reference:[8] Ganie, H. A.: On distance Laplacian spectrum (energy) of graphs.Discrete Math. Algorithms Appl. 12 (2020), Article ID 2050061, 16 pages. Zbl 1457.05064, MR 4157019, 10.1142/S1793830920500615; reference:[9] Ganie, H. A.: On the distance Laplacian energy ordering of tree.Appl. Math. Comput. 394 (2021), Article ID 125762, 10 pages. Zbl 1462.05222, MR 4182919, 10.1016/j.amc.2020.125762; reference:[10] Ganie, H. A., Chat, B. A., Pirzada, S.: Signless Laplacian energy of a graph and energy of line graph.Linear Algebra Appl. 544 (2018), 306-324. Zbl 1388.05114, MR 3765789, 10.1016/j.laa.2018.01.021; reference:[11] Ganie, H. A., Pirzada, S., Rather, B. A., Trevisan, V.: Further developments on Brouwer's conjecture for the sum of Laplacian eigenvalues of graphs.Linear Algebra Appl. 588 (2020), 1-18. Zbl 1437.05139, MR 4037607, 10.1016/j.laa.2019.11.020; reference:[12] Gutman, I., Zhou, B.: Laplacian energy of a graph.Linear Algebra Appl. 414 (2006), 29-37. Zbl 1092.05045, MR 2209232, 10.1016/j.laa.2005.09.008; reference:[13] Indulal, G., Gutman, I., Vijayakumar, A.: On distance energy of graphs.MATCH Commun. Math. Comput. Chem. 60 (2008), 461-472. Zbl 1199.05226, MR 2457864; reference:[14] Li, X., Shi, Y., Gutman, I.: Graph Energy.Springer, New York (2012). Zbl 1262.05100, MR 2953171, 10.1007/978-1-4614-4220-2; reference:[15] Monsalve, J., Rada, J.: Oriented bipartite graphs with minimal trace norm.Linear Multilinear Algebra 67 (2019), 1121-1131. Zbl 1411.05172, MR 3937031, 10.1080/03081087.2018.1448051; reference:[16] Pirzada, S.: An Introduction to Graph Theory.Orient Blackswan, Hyderabad (2012).; reference:[17] Pirzada, S., Ganie, H. A.: On the Laplacian eigenvalues of a graph and Laplacian energy.Linear Algebra Appl. 486 (2015), 454-468. Zbl 1327.05157, MR 3401774, 10.1016/j.laa.2015.08.032; reference:[18] Yang, J., You, L., Gutman, I.: Bounds on the distance Laplacian energy of graphs.Kragujevac J. Math. 37 (2013), 245-255. Zbl 1299.05236, MR 3150862

الاتاحة: http://hdl.handle.net/10338.dmlcz/151661

المؤلفون: Lamač, Jan, Vlasák, Miloslav

مصطلحات موضوعية: keyword:cycle cover, keyword:2-factor, keyword:Hamiltonian cycle, keyword:incidence matrix, keyword:least-square method, msc:05C38, msc:05C50, msc:93E24

وصف الملف: application/pdf

الاتاحة: http://hdl.handle.net/10338.dmlcz/703192

المؤلفون: Guterman, Alexander, Kreines, Elena, Vlasov, Alexander

مصطلحات موضوعية: keyword:tropical linear algebra, keyword:cyclicity index, keyword:linear transformations, msc:05C22, msc:05C38, msc:05C50

وصف الملف: application/pdf

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الاتاحة: http://hdl.handle.net/10338.dmlcz/151299

المؤلفون: Ma, Li

مصطلحات موضوعية: keyword:Bochner formula, keyword:heat equation, keyword:global solution, keyword:stochastic completeness, keyword:porous-media equation, keyword:McKean type estimate, msc:05C50, msc:35Jxx, msc:53Cxx, msc:58J35, msc:68R10

وصف الملف: application/pdf

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الاتاحة: http://hdl.handle.net/10338.dmlcz/150663

المؤلفون: Bart, Harm, Ehrhardt, Torsten

مصطلحات موضوعية: keyword:additive decomposition, keyword:rank constraint, keyword:zero pattern constraint, keyword:directed bipartite graph, keyword:$ß{L}$-free directed bipartite graph, keyword:permutation $ß{L}$-free directed bipartite graph, keyword:Bell number, keyword:Stirling partition number, msc:05C20, msc:05C50, msc:15A03, msc:15A21

وصف الملف: application/pdf

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الاتاحة: http://hdl.handle.net/10338.dmlcz/150620

المؤلفون: Wen, Fei, Huang, Qiongxiang

مصطلحات موضوعية: keyword:unicyclic graph, keyword:Laplacian eigenvalue, keyword:multiplicity, keyword:bound, msc:05C50

وصف الملف: application/pdf

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الاتاحة: http://hdl.handle.net/10338.dmlcz/150407

المؤلفون: Gao, Wei

مصطلحات موضوعية: keyword:graph, keyword:Randić matrix, keyword:Randić energy, msc:05C09, msc:05C50, msc:05C92

وصف الملف: application/pdf

Relation: mr:MR4389120; zbl:Zbl 07511567; reference:[1] Allem, L. E., Braga, R. O., Pastine, A.: Randić index and energy.MATCH Commun. Math. Comput. Chem. 83 (2020), 611-622.; reference:[2] Allem, L. E., Molina, G., Pastine, A.: Short note on Randić energy.MATCH Commun. Math. Comput. Chem. 82 (2019), 515-528. MR 3645368; reference:[3] Bozkurt, Ş. B., Güngör, A. D., Gutman, I.: Randić spectral radius and Randić energy.MATCH Commun. Math. Comput. Chem. 64 (2010), 321-334. Zbl 1265.05351, MR 2759776; reference:[4] Bozkurt, Ş. B., Güngör, A. D., Gutman, I., Çevik, A. S.: Randić matrix and Randić energy.MATCH Commun. Math. Comput. Chem. 64 (2010), 239-250. Zbl 1265.05113, MR 2677585; reference:[5] Das, K. C., Sorgun, S.: On Randić energy of graphs.MATCH Commun. Math. Comput. Chem. 72 (2014), 227-238. Zbl 06704610, MR 3241662; reference:[6] Das, K. C., Sorgun, S., Gutman, I.: On Randić energy.MATCH Commun. Math. Comput. Chem. 73 (2015), 81-92. Zbl 06749505, MR 3362137; reference:[7] Gutman, I., Furtula, B., Bozkurt, Ş. B.: On Randić energy.Linear Algebra Appl. 442 (2014), 50-57. Zbl 1282.05118, MR 3134349, 10.1016/j.laa.2013.06.010; reference:[8] He, J., Liu, Y.-M., Tian, J.-K.: Note on the Randić energy of graphs.Kragujevac J. Math. 42 (2018), 209-215. MR 3811340, 10.5937/kgjmath1802209j

الاتاحة: http://hdl.handle.net/10338.dmlcz/149587

المؤلفون: Ramezani, Farzaneh, Rowlinson, Peter, Stanić, Zoran

مصطلحات موضوعية: keyword:signed graph, keyword:join, keyword:adjacency matrix, keyword:main eigenvalue, keyword:net-degree, keyword:association scheme, msc:05C22, msc:05C50

وصف الملف: application/pdf

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الاتاحة: http://hdl.handle.net/10338.dmlcz/149573

المؤلفون: Kim, Sooyeong, Kirkland, Steve

مصطلحات موضوعية: keyword:algebraic connectivity, keyword:Fiedler vector, keyword:minimum degree, msc:05C50, msc:15A18

وصف الملف: application/pdf

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الاتاحة: http://hdl.handle.net/10338.dmlcz/149239

المؤلفون: Belardo, Francesco, Brunetti, Maurizio, Ciampella, Adriana

مصطلحات موضوعية: keyword:signed graph, keyword:spectral radius, keyword:bicyclic graph, msc:05C22, msc:05C50

وصف الملف: application/pdf

Relation: mr:MR4263178; zbl:07361077; reference:[1] Akbari, S., Belardo, F., Dodongeh, E., Nematollahi, M. A.: Spectral characterizations of signed cycles.Linear Algebra Appl. 553 (2018), 307-327. Zbl 1391.05126, MR 3809382, 10.1016/j.laa.2018.05.012; reference:[2] Akbari, S., Belardo, F., Heydari, F., Maghasedi, M., Souri, M.: On the largest eigenvalue of signed unicyclic graphs.Linear Algebra Appl. 581 (2019), 145-162. Zbl 1420.05070, MR 3982012, 10.1016/j.laa.2019.06.016; reference:[3] Akbari, S., Haemers, W. H., Maimani, H. R., Majd, L. Parsaei: Signed graphs cospectral with the path.Linear Algebra Appl. 553 (2018), 104-116. Zbl 1391.05156, MR 3809370, 10.1016/j.laa.2018.04.021; reference:[4] Belardo, F., Brunetti, M.: Connected signed graphs $L$-cospectral to signed $\infty$-graphs.Linear Multilinear Algebra 67 (2019), 2410-2426. Zbl 1425.05067, MR 4017722, 10.1080/03081087.2018.1494122; reference:[5] Belardo, F., Brunetti, M., Ciampella, A.: Signed bicyclic graphs minimizing the least Laplacian eigenvalue.Linear Algebra Appl. 557 (2018), 201-233. Zbl 1396.05066, MR 3848268, 10.1016/j.laa.2018.07.026; reference:[6] Belardo, F., Cioabă, S., Koolen, J., Wang, J.: Open problems in the spectral theory of signed graphs.Art Discrete Appl. Math. 1 (2018), Article ID P2.10, 23 pages. Zbl 1421.05052, MR 3997096, 10.26493/2590-9770.1286.d7b; reference:[7] Belardo, F., Marzi, E. M. Li, Simić, S. K.: Some results on the index of unicyclic graphs.Linear Algebra Appl. 416 (2006), 1048-1059. Zbl 1092.05043, MR 2242480, 10.1016/j.laa.2006.01.008; reference:[8] Brualdi, R. A., Solheid, E. S.: On the spectral radius of connected graphs.Publ. Inst. Math., Nouv. Sér. 39 (1986), 45-54. Zbl 0603.05028, MR 0869175; reference:[9] Brunetti, M.: On the existence of non-golden signed graphs.Atti Accad. Peloritana Pericolanti, Cl. Sci. Fis. Mat. Nat. 96 (2018), Article A2, 10 pages. MR 3900933, 10.1478/AAPP.96S2A2; reference:[10] Chang, A., Tian, F., Yu, A.: On the index of bicyclic graphs with perfect matchings.Discrete Math. 283 (2004), 51-59. Zbl 1064.05118, MR 2060353, 10.1016/j.disc.2004.02.005; reference:[11] Cvetković, D., Rowlinson, P.: Spectra of unicyclic graphs.Graphs Comb. 3 (1987), 7-23. Zbl 0623.05038, MR 0932109, 10.1007/BF01788525; reference:[12] Cvetković, D., Rowlinson, P., Simić, S.: Eigenspaces of Graphs.Encyclopedia of Mathematics and Its Applications 66. Cambridge University Press, Cambridge (1997). Zbl 0878.05057, MR 1440854, 10.1017/CBO9781139086547; reference:[13] Guo, S.-G.: The spectral radius of unicyclic and bicyclic graphs with $n$ vertices and $k$ pendant vertices.Linear Algebra Appl. 408 (2005), 78-85. Zbl 1073.05550, MR 2166856, 10.1016/j.laa.2005.05.022; reference:[14] Guo, S.-G.: On the spectral radius of bicyclic graphs with $n$ vertices and diameter $d$.Linear Algebra Appl. 422 (2007), 119-132. Zbl 1112.05064, MR 2298999, 10.1016/j.laa.2006.09.011; reference:[15] McKee, J., Smyth, C.: Integer symmetric matrices having all their eigenvalues in the interval $[-2, 2]$.J. Algebra 317 (2007), 260-290. Zbl 1140.15007, MR 2360149, 10.1016/j.jalgebra.2007.05.019; reference:[16] Simić, S. K.: On the largest eigenvalue of unicyclic graphs.Publ. Inst. Math., Nouv. Sér. 42 (1987), 13-19. Zbl 0641.05040, MR 0937447; reference:[17] Simić, S. K.: On the largest eigenvalue of bicyclic graphs.Publ. Inst. Math., Nouv. Sér. 46 (1989), 1-6. Zbl 0747.05058, MR 1060049; reference:[18] Stanić, Z.: Bounding the largest eigenvalue of signed graphs.Linear Algebra Appl. 573 (2019), 80-89. Zbl 1411.05109, MR 3933292, 10.1016/j.laa.2019.03.011; reference:[19] Stevanović, D.: Spectral Radius of Graphs.Elsevier Academic Press, Amsterdam (2015). Zbl 1309.05001, 10.1016/c2014-0-02233-2; reference:[20] Yu, A., Tian, F.: On the spectral radius of bicyclic graphs.MATCH Commun. Math. Comput. Chem. 52 (2004), 91-101. Zbl 1080.05522, MR 2104641; reference:[21] Zaslavsky, T.: Biased graphs. I: Bias, balance, and gains.J. Comb. Theory, Ser. B 47 (1989), 32-52. Zbl 0714.05057, MR 1007712, 10.1016/0095-8956(89)90063-4; reference:[22] Zaslavsky, T.: Matrices in the theory of signed simple graphs.Advances in Discrete Mathematics and Applications Ramanujan Mathematical Society Lecture Notes Series 13. Ramanujan Mathematical Society, Mysore (2010), 207-229. Zbl 1231.05120, MR 2766941; reference:[23] Zaslavsky, T.: A mathematical bibliography of signed and gain graphs and allied areas.Electron. J. Comb., Dynamic Surveys 5 (1998), Article ID DS8, 127 pages. Zbl 0898.05001, MR 1744869, 10.37236/29; reference:[24] Zaslavsky, T.: Glossary of signed and gain graphs and allied areas.Electron. J. Comb., Dynamic Survey 5 (1998), Article ID DS9, 41 pages. Zbl 0898.05002, MR 1744870, 10.37236/31

الاتاحة: http://hdl.handle.net/10338.dmlcz/148913

المؤلفون: Chen, Xiaodan, Liu, Xiaoqian

مصطلحات موضوعية: keyword:graph energy, keyword:vertex cover number, keyword:matching number, keyword:bound, msc:05C50

وصف الملف: application/pdf

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الاتاحة: http://hdl.handle.net/10338.dmlcz/148905

المؤلفون: Mehatari, Ranjit, Kannan, M. Rajesh

مصطلحات موضوعية: keyword:adjacency matrix, keyword:Laplacian matrix, keyword:normalized adjacency matrix, keyword:spectral radius, keyword:algebraic connectivity, keyword:Randić index, msc:05C50

وصف الملف: application/pdf

Relation: mr:MR4226479; zbl:07332714; reference:[1] Banerjee, A., Mehatari, R.: An eigenvalue localization theorem for stochastic matrices and its application to Randić matrices.Linear Algebra Appl. 505 (2016), 85-96. Zbl 1338.15069, MR 3506485, 10.1016/j.laa.2016.04.023; reference:[2] Bollobás, B., Erdös, P.: Graphs of extremal weights.Ars Comb. 50 (1998), 225-233. Zbl 0963.05068, MR 1670561; reference:[3] Bondy, J. A., Murty, U. S. R.: Graph Theory with Applications.American Elsevier, New York (1976). Zbl 1226.05083, MR 0411988; reference:[4] Bozkurt, Ş. B., Güngör, A. D., Gutman, I., Çevik, A. S.: Randić matrix and Randić energy.MATCH Commun. Math. Comput. Chem. 64 (2010), 239-250. Zbl 1265.05113, MR 2677585; reference:[5] Brouwer, A. E., Haemers, W. H.: Spectra of Graphs.Universitext. Springer, Berlin (2012). Zbl 1231.05001, MR 2882891, 10.1007/978-1-4614-1939-6; reference:[6] Butler, S., Chung, F.: Spectral graph theory.Handbook of Linear Algebra L. Hogben Discrete Mathematics and its Applications. CRC Press, Boca Raton (2014), Article ID 47. Zbl 1284.15001, MR 3013937; reference:[7] Cavers, M. S.: The normalized Laplacian matrix and general Randić index of graphs: Ph.D. Thesis.University of Regina, Regina (2010). MR 3078627; reference:[8] Chung, F. R. K.: Spectral Graph Theory.Regional Conference Series in Mathematics 92. American Mathematical Society, Providence (1997). Zbl 0867.05046, MR 1421568; reference:[9] Cvetković, D., Doob, M., Sachs, H.: Spectra of Graphs: Theory and Applications.Pure and Applied Mathematics 87. Academic Press, New York (1980). Zbl 0458.05042, MR 0572262; reference:[10] Das, K. C.: A sharp upper bound for the number of spanning trees of a graph.Graphs Comb. 23 (2007), 625-632. Zbl 1139.05032, MR 2365415, 10.1007/s00373-007-0758-4; reference:[11] Fiedler, M.: Algebraic connectivity of graphs.Czech. Math. J. 23 (1973), 298-305. Zbl 0265.05119, MR 0318007, 10.21136/CMJ.1973.101168; reference:[12] Li, J., Guo, J-M., Shiu, W. C.: Bounds on normalized Laplacian eigenvalues of graphs.J. Inequal. Appl. 316 (2014), Article ID 316, 8 pages. Zbl 1332.05090, MR 3344113, 10.1186/1029-242X-2014-316; reference:[13] Marsli, R., Hall, F. J.: On bounding the eigenvalues of matrices with constant row-sums.Linear Multilinear Algebra 67 (2019), 672-684. Zbl 1412.15020, MR 3914323, 10.1080/03081087.2018.1430736; reference:[14] Randić, M.: Characterization of molecular branching.J. Am. Chem. Soc. 97 (1975), 6609-6615. 10.1021/ja00856a001; reference:[15] Rojo, O., Soto, R. L.: A new upper bound on the largest normalized Laplacian eigenvalue.Oper. Matrices 7 (2013), 323-332. Zbl 1283.05168, MR 3099188, 10.7153/oam-07-19; reference:[16] Stanić, Z.: Inequalities for Graph Eigenvalues.London Mathematical Society Lecture Note Series 423. Cambridge University Press, Cambridge (2015). Zbl 1368.05001, MR 3469535, 10.1017/CBO9781316341308; reference:[17] Varga, R. S.: Geršgorin and His Circles.Springer Series in Computational Mathematics 36. Springer, Berlin (2004). Zbl 1057.15023, MR 2093409, 10.1007/978-3-642-17798-9; reference:[18] Wolkowicz, H., Styan, G. P. H.: Bounds for eigenvalues using traces.Linear Algebra Appl. 29 (1980), 471-506. Zbl 0435.15015, MR 0562777, 10.1016/0024-3795(80)90258-X

الاتاحة: http://hdl.handle.net/10338.dmlcz/148737

المؤلفون: Andelić, Milica, Du, Zhibin, da Fonseca, Carlos M., Simić, Slobodan K.

مصطلحات موضوعية: keyword:tridiagonal matrix, keyword:threshold graph, keyword:chain graph, keyword:eigenvalue-free interval, msc:05C50

وصف الملف: application/pdf

Relation: mr:MR4181801; zbl:07285984; reference:[1] Aguilar, C. O., Lee, J.-Y., Piato, E., Schweitzer, B. J.: Spectral characterizations of anti-regular graphs.Linear Algebra Appl. 557 (2018), 84-104. Zbl 1396.05064, MR 3848263, 10.1016/j.laa.2018.07.028; reference:[2] Alazemi, A., elić, M. Anđ, Simić, S. K.: Eigenvalue location for chain graphs.Linear Algebra Appl. 505 (2016), 194-210. Zbl 1338.05155, MR 3506491, 10.1016/j.laa.2016.04.030; reference:[3] elić, M. Anđ, Andrade, E., Cardoso, D. M., Fonseca, C. M. da, Simić, S. K., Tošić, D. V.: Some new considerations about double nested graphs.Linear Algebra Appl. 483 (2015), 323-341. Zbl 1319.05084, MR 3378905, 10.1016/j.laa.2015.06.010; reference:[4] elić, M. Anđ, Fonseca, C. M. da: Sufficient conditions for positive definiteness of tridiagonal matrices revisited.Positivity 15 (2011), 155-159 \99999DOI99999 10.1007/s11117-010-0047-y \goodbreak. Zbl 1216.15022, MR 2782752, 10.1007/s11117-010-0047-y; reference:[5] elić, M. Anđ, Ghorbani, E., Simić, S. K.: Vertex types in threshold and chain graphs.Discrete Appl. Math. 269 (2019), 159-168. Zbl 1421.05062, MR 4016594, 10.1016/j.dam.2019.02.040; reference:[6] elić, M. Anđ, Simić, S. K., Živković, D., Dolićanin, E. Ć.: Fast algorithms for computing the characteristic polynomial of threshold and chain graphs.Appl. Math. Comput. 332 (2018), 329-337. Zbl 1427.05127, MR 3788693, 10.1016/j.amc.2018.03.024; reference:[7] Cvetković, D., Rowlinson, P., Simić, S.: An Introduction to the Theory of Graph Spectra.London Mathematical Society Student Texts 75, Cambridge University Press, Cambridge (2010). Zbl 1211.05002, MR 2571608, 10.1017/CBO9780511801518; reference:[8] Fonseca, C. M. da: On the eigenvalues of some tridiagonal matrices.J. Comput. Appl. Math. 200 (2007), 283-286. Zbl 1119.15012, MR 2276832, 10.1016/j.cam.2005.08.047; reference:[9] Ghorbani, E.: Eigenvalue-free interval for threshold graphs.Linear Algebra Appl. 583 (2019), 300-305. Zbl 1426.05096, MR 4002158, 10.1016/j.laa.2019.08.028; reference:[10] Jacobs, D. P., Trevisan, V., Tura, F.: Eigenvalues and energy in threshold graphs.Linear Algebra Appl. 465 (2015), 412-425. Zbl 1302.05103, MR 3274686, 10.1016/j.laa.2014.09.043; reference:[11] Lazzarin, J., Márquez, O. F., Tura, F. C.: No threshold graphs are cospectral.Linear Algebra Appl. 560 (2019), 133-145. Zbl 1401.05152, MR 3866549, 10.1016/j.laa.2018.09.033; reference:[12] Maybee, J. S., Olesky, D. D., Driessche, P. van den, Wiener, G.: Matrices, digraphs, and determinants.SIAM J. Matrix Anal. Appl. 10 (1989), 500-519. Zbl 0701.05038, MR 1016799, 10.1137/0610036

الاتاحة: http://hdl.handle.net/10338.dmlcz/148416

المؤلفون: Stanić, Zoran

مصطلحات موضوعية: keyword:main angle, keyword:signed graph, keyword:adjacency matrix, keyword:Laplacian matrix, keyword:Gram matrix, msc:05C22, msc:05C50

وصف الملف: application/pdf

Relation: mr:MR4181798; zbl:07285981; reference:[1] Cardoso, D. M., Sciriha, I., Zerafa, C.: Main eigenvalues and $(\kappa, \tau)$-regular sets.Linear Algebra Appl. 432 (2010), 2399-2408. Zbl 1217.05136, MR 2599869, 10.1016/j.laa.2009.07.039; reference:[2] Cvetković, D., Doob, M., Sachs, H.: Spectra of Graphs: Theory and Applications.J. A. Barth Verlag, Heidelberg (1995). Zbl 0824.05046, MR 1324340; reference:[3] Cvetković, D., Rowlinson, P., Simić, S.: An Introduction to the Theory of Graph Spectra.London Mathematical Society Student Texts 75, Cambridge University Press, Cambridge (2010). Zbl 1211.05002, MR 2571608, 10.1017/CBO9780511801518; reference:[4] Deng, H., Huang, H.: On the main signless Laplacian eigenvalues of a graph.Electron. J. Linear Algebra 26 (2013), 381-393. Zbl 1282.05109, MR 3084649, 10.13001/1081-3810.1659; reference:[5] Doob, M.: A geometric interpretation of the least eigenvalue of a line graph.Combinatorial Mathematics and its Applications R. C. Bose, T. A. Dowling University of North Carolina, Chapel Hill (1970), 126-135. Zbl 0209.55403, MR 0268060; reference:[6] Haynsworth, E. V.: Applications of a theorem on partitioned matrices.J. Res. Natl. Bur. Stand., Sec. B 63 (1959), 73-78. Zbl 0090.24104, MR 0109432, 10.6028/jres.063B.009; reference:[7] Hou, Y., Tang, Z., Shiu, W. C.: Some results on graphs with exactly two main eigenvalues.Appl. Math. Lett. 25 (2012), 1274-1278. Zbl 1248.05112, MR 2947393, 10.1016/j.aml.2011.11.025; reference:[8] Hou, Y., Zhou, H.: Trees with exactly two main eigenvalues.J. Nat. Sci. Hunan Norm. Univ. 28 (2005), 1-3 Chinese. Zbl 1109.05071, MR 2240441; reference:[9] Petersdorf, M., Sachs, H.: Über Spektrum, Automorphismengruppe und Teiler eines Graphen.Wiss. Z. Tech. Hochsch. Ilmenau 15 (1969), 123-128 German. Zbl 0199.27504, MR 0269552; reference:[10] Rowlinson, P.: The main eigenvalues of a graph: A survey.Appl. Anal. Discrete Math. 1 (2007), 445-471. Zbl 1199.05241, MR 2355287, 10.2298/AADM0702445R; reference:[11] Stanić, Z.: Inequalities for Graph Eigenvalues.London Mathematical Society Lecture Note Series 423, Cambridge University Press, Cambridge (2015). Zbl 1368.05001, MR 3469535, 10.1017/CBO9781316341308; reference:[12] Stanić, Z.: Bounding the largest eigenvalue of signed graphs.Linear Algebra Appl. 573 (2019), 80-89. Zbl 1411.05109, MR 3933292, 10.1016/j.laa.2019.03.011; reference:[13] Zaslavsky, T.: Matrices in the theory of signed simple graphs.Advances in Discrete Mathematics and Applications B. D. Acharya, G. O. H. Katona, J. Nešetřil Ramanujan Mathematical Society Lecture Notes Series 13, Ramanujan Mathematical Society, Mysore (2010), 207-229. Zbl 1231.05120, MR 2766941

الاتاحة: http://hdl.handle.net/10338.dmlcz/148413

المؤلفون: Rocha, Israel

مصطلحات موضوعية: keyword:sum of eigenvalues, keyword:graph energy, keyword:random matrix, msc:05C50, msc:15A18

وصف الملف: application/pdf

Relation: mr:MR4160784; zbl:07285948; reference:[1] Das, K. C., Mojallal, S. A., Sun, S.: On the sum of the $k$ largest eigenvalues of graphs and maximal energy of bipartite graphs.Linear Algebra Appl. 569 (2019), 175-194. Zbl 1411.05156, MR 3904318, 10.1016/j.laa.2019.01.016; reference:[2] Füredi, Z., Komlós, J.: The eigenvalues of random symmetric matrices.Combinatorica 1 (1981), 233-241. Zbl 0494.15010, MR 0637828, 10.1007/BF02579329; reference:[3] Graovac, A., Gotman, I., Trinajstić, N.: Topological Approach to the Chemistry of Conjugated Molecules.Lecture Notes in Chemistry 4. Springer, Berlin (1977). Zbl 0385.05032, 10.1007/978-3-642-93069-0; reference:[4] Hoeffding, W.: Probability inequalities for sums of bounded random variables.J. Am. Stat. Assoc. 58 (1963), 13-30. Zbl 0127.10602, MR 0144363, 10.2307/2282952; reference:[5] Li, X., Shi, Y., Gutman, I.: Graph Energy.Springer, New York (2012). Zbl 1262.05100, MR 2953171, 10.1007/978-1-4614-4220-2; reference:[6] Mohar, B.: On the sum of $k$ largest eigenvalues of graphs and symmetric matrices.J. Comb. Theory, Ser. B 99 (2009), 306-313. Zbl 1217.05151, MR 2482950, 10.1016/j.jctb.2008.07.001; reference:[7] Nikiforov, V.: The energy of graphs and matrices.J. Math. Anal. Appl. 326 (2007), 1472-1475. Zbl 1113.15016, MR 2280998, 10.1016/j.jmaa.2006.03.072; reference:[8] Nikiforov, V.: On the sum of $k$ largest singular values of graphs and matrices.Linear Algebra Appl. 435 (2011), 2394-2401. Zbl 1222.05172, MR 2811124, 10.1016/j.laa.2010.08.014; reference:[9] Nikiforov, V.: Beyond graph energy: norms of graphs and matrices.Linear Algebra Appl. 506 (2016), 82-138. Zbl 1344.05089, MR 3530671, 10.1016/j.laa.2016.05.011; reference:[10] Rocha, I.: Brouwer's conjecture holds asymptotically almost surely.Linear Algebra Appl. 597 (2020), 198-205. Zbl 07190773, MR 4082064, 10.1016/j.laa.2020.03.019; reference:[11] Wigner, E. P.: On the distribution of the roots of certain symmetric matrices.Ann. Math. (2) 67 (1958), 325-327. Zbl 0085.13203, MR 0095527, 10.2307/1970008

الاتاحة: http://hdl.handle.net/10338.dmlcz/148368

المؤلفون: Ramamurthy, Balaji, Bapat, Ravindra Bhalchandra, Goel, Shivani

مصطلحات موضوعية: keyword:tree, keyword:Laplacian matrix, keyword:inertia, keyword:Haynsworth formula, msc:05C50, msc:15B48

وصف الملف: application/pdf

Relation: mr:MR4160783; zbl:07285947; reference:[1] Balaji, R., Bapat, R. B.: Block distance matrices.Electron. J. Linear Algebra 16 (2007), 435-443. Zbl 1148.15016, MR 2365897, 10.13001/1081-3810.1213; reference:[2] Bapat, R. B.: Determinant of the distance matrix of a tree with matrix weights.Linear Algebra Appl. 416 (2006), 2-7. Zbl 1108.15006, MR 2232916, 10.1016/j.laa.2005.02.022; reference:[3] Bapat, R., Kirkland, S. J., Neumann, M.: On distance matrices and Laplacians.Linear Algebra Appl. 401 (2005), 193-209. Zbl 1064.05097, MR 2133282, 10.1016/j.laa.2004.05.011; reference:[4] Fiedler, M.: Matrices and Graphs in Geometry.Encyclopedia of Mathematics and Its Applications 139. Cambridge University Press, Cambridge (2011). Zbl 1225.51017, MR 2761077, 10.1017/CBO9780511973611; reference:[5] Fiedler, M., Markham, T. L.: Completing a matrix when certain entries of its inverse are specified.Linear Algebra Appl. 74 (1986), 225-237. Zbl 0592.15002, MR 0822149, 10.1016/0024-3795(86)90125-4

الاتاحة: http://hdl.handle.net/10338.dmlcz/148367