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1Academic Journal
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
Relation: mr:MR4389106; zbl:Zbl 07511553; reference:[1] elić, M. Anđ, Koledin, T., Stanić, Z.: On regular signed graphs with three eigenvalues.Discuss. Math., Graph Theory 40 (2020), 405-416. Zbl 1433.05139, MR 4060992, 10.7151/dmgt.2279; reference:[2] Belardo, F., Cioabă, S. M., 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:[3] Belardo, F., Simić, S. K.: On the Laplacian coefficients of signed graphs.Linear Algebra Appl. 475 (2015), 94-113. Zbl 1312.05078, MR 3325220, 10.1016/j.laa.2015.02.007; reference:[4] Chan, H. C., Rodger, C. A., Seberry, J.: On inequivalent weighing matrices.Ars Comb. 21A (1986), 299-333. Zbl 0599.05013, MR 0835757; reference:[5] Cheng, X.-M., Gavrilyuk, A. L., Greaves, G. R. W., Koolen, J. H.: Biregular graphs with three eigenvalues.Eur. J. Comb. 56 (2016), 57-80. Zbl 1335.05107, MR 3490095, 10.1016/j.ejc.2016.03.004; reference:[6] Cheng, X.-M., Greaves, G. R. W., Koolen, J. H.: Graphs with three eigenvalues and second largest eigenvalue at most 1.J. Comb. Theory, Ser. B 129 (2018), 55-78. Zbl 1379.05072, MR 3758241, 10.1016/j.jctb.2017.09.004; reference:[7] Colbourn, C. J., (eds.), J. H. Dinitz: Handbook of Combinatorial Designs.Discrete Mathematics and its Applications. Chapman & Hall/CRC, Boca Raton (2007). Zbl 1101.05001, MR 2246267, 10.1201/9781420010541; reference:[8] Cvetković, D., Doob, M., Sachs, H.: Spectra of Graphs: Theory and Applications.J. A. Barth, Leipzig (1995). Zbl 0824.05046, MR 1324340; reference:[9] 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:[10] Harada, M., Munemasa, A.: On the classification of weighing matrices and self-orthogonal codes.J. Comb. Des. 20 (2012), 45-57. Zbl 1252.05026, MR 2864617, 10.1002/jcd.20295; reference:[11] Hou, Y., Tang, Z., Wang, D.: On signed graphs with just two distinct adjacency eigenvalues.Discrete Math. 342 (2019), Article ID 111615, 8 pages. Zbl 1422.05049, MR 3990025, 10.1016/j.disc.2019.111615; reference:[12] 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:[13] Ramezani, F.: On the signed graphs with two distinct eigenvalues.Util. Math. 114 (2020), 33-48. Zbl 07274222, MR 4230326; reference:[14] Ramezani, F.: Some regular signed graphs with only two distinct eigenvalues.(to appear) in Linear Multilinear Algebra. MR 4388842, 10.1080/03081087.2020.1736979; reference:[15] Ramezani, F., Rowlinson, P., Stanić, Z.: On eigenvalue multiplicity in signed graphs.Discrete Math. 343 (2020), Article ID 111982, 8 pages. Zbl 07233221, MR 4107756, 10.1016/j.disc.2020.111982; reference:[16] Rowlinson, P.: Certain 3-decompositions of complete graphs, with an application to finite fields.Proc. R. Soc. Edinb., Sect. A 99 (1985), 277-281. Zbl 0562.05044, MR 0785534, 10.1017/S0308210500014293; reference:[17] Rowlinson, P.: On graphs with just three distinct eigenvalues.Linear Algebra Appl. 507 (2016), 462-473. Zbl 1343.05096, MR 3536969, 10.1016/j.laa.2016.06.031; reference:[18] Rowlinson, P.: More on graphs with just three distinct eigenvalues.Appl. Anal. Discrete Math. 11 (2017), 74-80. MR 3648655, 10.2298/AADM161111033R; reference:[19] Seidel, J. J.: Graphs and two-graphs.Proceedings of the 5th Southeastern Conference on Combinatorics, Graph Theory, and Computing Utilitas Mathematica Publication, Winnipeg (1974), 125-143. Zbl 0308.05120, MR 0364028; reference:[20] Simić, S. K., Stanić, Z.: Polynomial reconstruction of signed graphs.Linear Algebra Appl. 501 (2016), 390-408. Zbl 1334.05056, MR 3485074, 10.1016/j.laa.2016.03.036; reference:[21] Stanić, Z.: Regular Graphs: A Spectral Approach.De Gruyter Series in Discrete Mathematics and Applications 4. De Gruyter, Berlin (2017). Zbl 1370.05002, MR 3753662, 10.1515/9783110351347; reference:[22] Stanić, Z.: Integral regular net-balanced signed graphs with vertex degree at most four.Ars Math. Contemp. 17 (2019), 103-114. Zbl 1433.05142, MR 3998150, 10.26493/1855-3974.1740.803; reference:[23] Stanić, Z.: On strongly regular signed graphs.Discrete Appl. Math. 271 (2019), 184-190 corrigendum ibid. 284 640 2020. Zbl 1428.05331, MR 4030312, 10.1016/j.dam.2019.06.017; reference:[24] Stanić, Z.: Spectra of signed graphs with two eigenvalues.Appl. Math. Comput. 364 (2020), Article ID 124627, 9 pages. Zbl 1433.05210, MR 3996372, 10.1016/j.amc.2019.124627; reference:[25] Dam, E. R. van: Nonregular graphs with three eigenvalues.J. Comb. Theory, Ser. B 73 (1998), 101-118. Zbl 0917.05044, MR 1631983, 10.1006/jctb.1998.1815; reference:[26] Dam, E. R. van: Three-class association schemes.J. Algebr. Comb. 10 (1999), 69-107. Zbl 0929.05096, MR 1701285, 10.1023/A:1018628204156; reference:[27] Zaslavsky, T.: Signed graphs.Discrete Appl. Math. 4 (1982), 47-74. Zbl 0476.05080, MR 0676405, 10.1016/0166-218X(82)90033-6; reference:[28] 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
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2Academic Journal
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
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3Academic Journal
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
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4Academic Journal
المؤلفون: Panda, Swarup Kumar
مصطلحات موضوعية: keyword:adjacency matrix, keyword:unicyclic graph, keyword:bicyclic graph, keyword:inverse graph, keyword:perfect matching, msc:05C50, msc:15A09
وصف الملف: application/pdf
Relation: mr:MR3736023; zbl:Zbl 06819577; reference:[1] Akbari, S., Kirkland, S. J.: On unimodular graphs.Linear Algebra Appl. 421 (2007), 3-15. Zbl 1108.05060, MR 2290681, 10.1016/j.laa.2006.10.017; reference:[2] Barik, S., Neumann, M., Pati, S.: On nonsingular trees and a reciprocal eigenvalue property.Linear Multilinear Algebra 54 (2006), 453-465. Zbl 1119.05064, MR 2259602, 10.1080/03081080600792897; reference:[3] Buckley, F., Doty, L. L., Harary, F.: On graphs with signed inverses.Networks 18 (1988), 151-157. Zbl 0646.05061, MR 0953918, 10.1002/net.3230180302; reference:[4] Cvetković, D. M., Gutman, I., Simić, S. K.: On self-pseudo-inverse graphs.Publ. Elektroteh. Fak., Univ. Beogr., Ser. Mat. Fiz. (1978), 602-633, (1979), 111-117. Zbl 0437.05047, MR 0580431; reference:[5] Frucht, R., Harary, F.: On the corona of two graphs.Aequationes Mathematicae 4 (1970), 322-325. Zbl 0198.29302, MR 0281659, 10.1007/BF01844162; reference:[6] Godsil, C. D.: Inverses of trees.Combinatorica 5 (1985), 33-39. Zbl 0578.05049, MR 0803237, 10.1007/BF02579440; reference:[7] Harary, F.: On the notion of balance of a signed graph.Mich. Math. J. 2 (1953), 143-146. Zbl 0056.42103, MR 0067468, 10.1307/mmj/1028989917; reference:[8] Harary, F., Minc, H.: Which nonnegative matrices are self-inverse?.Math. Mag. 49 (1976), 91-92. Zbl 0321.15008, MR 0396629, 10.2307/2689442; reference:[9] Panda, S. K., Pati, S.: On the inverse of a class of bipartite graphs with unique perfect matchings.Electron. J. Linear Algebra 29 (2015), 89-101. Zbl 1323.05107, MR 3414587, 10.13001/1081-3810.2865; reference:[10] Panda, S. K., Pati, S.: On some graphs which possess inverses.Linear Multilinear Algebra 64 (2016), 1445-1459. Zbl 1341.05216, MR 3490639, 10.1080/03081087.2015.1091434; reference:[11] Pavlíková, S., Krč-Jediný, J.: On the inverse and the dual index of a tree.Linear Multilinear Algebra 28 (1990), 93-109. Zbl 0745.05018, MR 1077739, 10.1080/03081089008818034; reference:[12] Simion, R., Cao, D.-S.: Solution to a problem of C. D. Godsil regarding bipartite graphs with unique perfect matching.Combinatorica 9 (1989), 85-89. Zbl 0688.05056, MR 1010303, 10.1007/BF02122687; reference:[13] Tifenbach, R. M.: Strongly self-dual graphs.Linear Algebra Appl. 435 (2011), 3151-3167. Zbl 1226.05170, MR 2831603, 10.1016/j.laa.2011.05.010; reference:[14] Tifenbach, R. M., Kirkland, S. J.: Directed intervals and the dual of a graph.Linear Algebra Appl. 431 (2009), 792-807. Zbl 1226.05171, MR 2535551, 10.1016/j.laa.2009.03.032; reference:[15] Yates, K.: Hückel Molecular Orbital Theory.Academic Press (1978). 10.1016/b978-0-12-768850-3.x5001-9
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5Academic Journal
المؤلفون: Boza, Luis, Fedriani, Eugenio Manuel, Núñez, Juan, Pacheco, Ana María, Villar, María Trinidad
مصطلحات موضوعية: keyword:directed pseudo-graph, keyword:adjacency matrix, keyword:Lie algebra, msc:05C99, msc:17B30, msc:17B45, msc:17B50, msc:17B60
وصف الملف: application/pdf
Relation: mr:MR3247457; zbl:Zbl 06391489; reference:[1] Boza, L., Fedriani, E. M., Núñez, J.: The relation between oriented pseudo-graphs with multiple edges and some Lie algebras.Actas del IV Encuentro Andaluz de Matemática Discreta (2005), 99-104 Spanish.; reference:[2] Carriazo, A., Fernández, L. M., Núñez, J.: Combinatorial structures associated with Lie algebras of finite dimension.Linear Algebra Appl. 389 (2004), 43-61. Zbl 1053.05059, MR 2080394; reference:[3] Ceballos, M., Núñez, J., Tenorio, Á. F.: Complete triangular structures and Lie algebras.Int. J. Comput. Math. 88 (2011), 1839-1851. Zbl 1271.17015, MR 2810866, 10.1080/00207161003767994; reference:[4] Ceballos, M., Núñez, J., Tenorio, Á. F.: Study of Lie algebras by using combinatorial structures.Linear Algebra Appl. 436 (2012), 349-363. Zbl 1276.17010, MR 2854876; reference:[5] Ceballos, M., Núñez, J., Tenorio, A. F.: Combinatorial structures and Lie algebras of upper triangular matrices.Appl. Math. Lett. 25 (2012), 514-519. MR 2856025, 10.1016/j.aml.2011.09.049; reference:[6] Graaf, W. A. de: Classification of solvable Lie algebras.Exp. Math. 14 (2005), 15-25. Zbl 1173.17300, MR 2146516, 10.1080/10586458.2005.10128911; reference:[7] Fernández, L. M., Martín-Martínez, L.: Lie algebras associated with triangular configurations.Linear Algebra Appl. 407 (2005), 43-63. Zbl 1159.17302, MR 2161914; reference:[8] Gross, J. L., Yellen, J.: Handbook of Graph Theory.Discrete Mathematics and its Applications CRC Press, Boca Raton (2004). Zbl 1036.05001, MR 2035186; reference:[9] Hamelink, R. C.: Graph theory and Lie algebra.Many Facets of Graph Theory, Proc. Conf. Western Michigan Univ., Kalamazoo/Mi. 1968 Lect. Notes Math. 110 149-153 Springer, Berlin (1969). Zbl 0187.45504, MR 0256910, 10.1007/BFb0060113; reference:[10] Núñez, J., Pacheco, A., Villar, M. T.: Discrete mathematics applied to the treatment of some Lie theory problems.Sixth Conference on Discrete Mathematics and Computer Science Univ. Lleida, Lleida (2008), 485-492 Spanish (2008), 485-492. MR 2523385; reference:[11] Núñez, J., Pacheco, A. M., Villar, M. T.: Study of a family of Lie algebra over $\mathbb Z/3\mathbb Z$.Int. J. Math. Stat. 7 (2010), 40-45. MR 2755406; reference:[12] Patera, J., Zassenhaus, H.: Solvable Lie algebras of dimension $\leq 4$ over perfect fields.Linear Algebra Appl. 142 (1990), 1-17. MR 1077969; reference:[13] Varadarajan, V. S.: Lie Groups, Lie Algebras and Their Representations (Reprint of the 1974 edition).Graduate Texts in Mathematics 102 Springer, New York (1984). Zbl 0955.22500, MR 0746308, 10.1007/978-1-4612-1126-6
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6Academic Journal
المؤلفون: Tian, Gui-Xian, Huang, Ting-Zhu
مصطلحات موضوعية: keyword:graph, keyword:adjacency matrix, keyword:Laplacian matrix, keyword:spectral radius, keyword:bound, msc:05C50, msc:15A18
وصف الملف: application/pdf
Relation: mr:MR2990195; zbl:Zbl 1265.05418; reference:[1] Berman, A., Zhang, X.-D.: On the spectral radius of graphs with cut vertices.J. Combin. Theory, Ser. B 83 (2001), 233-240. Zbl 1023.05098, MR 1866719, 10.1006/jctb.2001.2052; reference:[2] Brankov, V., Hansen, P., Stevanović, D.: Automated cunjectures on upper bounds for the largest Laplacian eigenvalue of graphs.Linear Algebra Appl. 414 (2006), 407-424. MR 2213408; reference:[3] Cvetković, D., Doob, M., Sachs, H.: Spectra of Graphs. Theory and Application.Deutscher Verlag der Wissenschaften Berlin (1980). Zbl 0458.05042, MR 0572262; reference:[4] Das, K. C., Kumar, P.: Some new bounds on the spectral radius of graphs.Discrete Math. 281 (2004), 149-161. Zbl 1042.05060, MR 2047763, 10.1016/j.disc.2003.08.005; reference:[5] Favaron, O., Mahéo, M., Saclé, J.-F.: Some eigenvalue properties in graphs (Conjectures of Graffiti---II).Discrete Math. 111 (1993), 197-220. Zbl 0785.05065, MR 1210097, 10.1016/0012-365X(93)90156-N; reference:[6] Hofmeister, M.: Spectral radius and degree sequence.Math. Nachr. 139 (1988), 37-44. Zbl 0695.05046, MR 0978106, 10.1002/mana.19881390105; reference:[7] Hong, Y., Zhang, X.-D.: Sharp upper and lower bounds for largest eigenvalue of the Laplacian matrices of trees.Discrete Math. 296 (2005), 187-197. Zbl 1068.05044, MR 2154712, 10.1016/j.disc.2005.04.001; reference:[8] Liu, H., Lu, M.: Bounds for the Laplacian spectral radius of graphs.Linear Multilinear Algebra 58 (2010), 113-119. Zbl 1217.05148, MR 2641527, 10.1080/03081080802450021; reference:[9] Liu, H., Lu, M., Tian, F.: Some upper bounds for the energy of graphs.J. Math. Chem. 41 (2007), 45-57. Zbl 1110.92070, MR 2305216, 10.1007/s10910-006-9183-9; reference:[10] 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:[11] Shi, L.: Bounds on the (Laplacian) spectral radius of graphs.Linear Algebra Appl. 422 (2007), 755-770. Zbl 1113.05065, MR 2305155, 10.1016/j.laa.2006.12.003; reference:[12] Tian, G.-X., Huang, T.-Z., Zhou, B.: A note on sum of powers of the Laplacian eigenvalues of bipartite graphs.Linear Algebra Appl. 430 (2009), 2503-2510. Zbl 1165.05020, MR 2508309; reference:[13] Yu, A., Lu, M., Tian, F.: On the spectral radius of graphs.Linear Algebra Appl. 387 (2004), 41-49. Zbl 1041.05051, MR 2069267, 10.1016/j.laa.2004.01.020; reference:[14] Yu, A., Lu, M., Tian, F.: New upper bounds for the energy of graphs.MATCH Commun. Math. Comput. Chem. 53 (2005), 441-448. Zbl 1081.05067, MR 2134203; reference:[15] Zhou, B.: Energy of a graph.MATCH Commun. Math. Comput. Chem. 51 (2004), 111-118. Zbl 1106.05068, MR 2063930
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7Academic Journal
المؤلفون: Wang, Jianfeng, Zhao, Haixing, Huang, Qiongxiang
مصطلحات موضوعية: keyword:adjacency matrix, keyword:cospectral graph, keyword:spectral characteriztion, keyword:multicone graph, msc:05C50
وصف الملف: application/pdf
Relation: mr:MR2899739; zbl:Zbl 1249.05256; reference:[1] Cvetković, D ., Doob, M., Sachs, H.: Spectra of Graphs. Theory and Applications. 3rd revised a. enl. ed.J. A. Barth Verlag Leipzig (1995). MR 1324340; reference:[2] Cvetković, D., Doob, M., Simić, S.: Generalized line graphs.J. Graph Theory 5 (1981), 385-399. Zbl 0475.05061, MR 0635701, 10.1002/jgt.3190050408; reference:[3] Dam, E. R. van, Haemers, W. H.: Which graphs are determined by their spectrum?.Linear Algebra Appl. 373 (2003), 241-272. MR 2022290; reference:[4] Dam, E. R. van, Haemers, W. H.: Developments on spectral characterizations of graphs.Discrete Math. 309 (2009), 576-586. MR 2499010, 10.1016/j.disc.2008.08.019; reference:[5] Godsil, C. D., McKay, B. D.: Constructing cospectral graphs.Aequationes Math. 25 (1982), 257-268. Zbl 0527.05051, MR 0730486, 10.1007/BF02189621; reference:[6] Erdős, P., Rényi, A., Sós, V. T.: On a problem of graph theory.Stud. Sci. Math. Hung. 1 (1966), 215-235. MR 0223262; reference:[7] Günthard, Hs. H., Primas, H.: Zusammenhang von Graphtheorie und Mo-Theorie von Molekeln mit Systemen konjugierter Bindungen.Helv. Chim. Acta 39 (1956), 1645-1653. 10.1002/hlca.19560390623; reference:[8] Haemers, W. H., Spence, E.: Enumeration of cospectral graphs.Eur. J. Comb. 25 (2004), 199-211. Zbl 1033.05070, MR 2070541, 10.1016/S0195-6698(03)00100-8; reference:[9] Harary, F., King, C., Mowshowitz, A., Read, R.: Cospectral graphs and digraphs.Bull. Lond. Math. Soc. 3 (1971), 321-328. Zbl 0224.05125, MR 0294176, 10.1112/blms/3.3.321; reference:[10] Hong, Y., Shu, J.-L., Fang, K.: A sharp upper bound of the spectral radius of graphs.J. Comb. Theory, Ser. B 81 (2001), 177-183. Zbl 1024.05059, MR 1814902, 10.1006/jctb.2000.1997; reference:[11] Johnson, C. R., Newman, M.: A note on cospectral graphs.J. Comb. Theory, Ser. B 28 (1980), 96-103. Zbl 0431.05021, MR 0565513, 10.1016/0095-8956(80)90058-1; reference:[12] Nikiforov, V.: Some inequalities for the largest eigenvalue of a graph.Comb. Probab. Comput. 11 (2002), 179-189. Zbl 1005.05029, MR 1888908, 10.1017/S0963548301004928; reference:[13] Zhou, B., Cho, H. H.: Remarks on spectral radius and Laplacian eigenvalues of a graph.Czech. Math. J. 55 (130) (2005), 781-790. Zbl 1081.05068, MR 2153101, 10.1007/s10587-005-0064-3; reference:[14] Wang, J. F., Belardo, F., Huang, Q. X., Borovićanin, B.: On the two largest Q-eigenvalues of graphs.Discrete Math. 310 (2010), 2858-2866. Zbl 1208.05079, MR 2677645, 10.1016/j.disc.2010.06.030; reference:[15] Wilf, H. S.: The friendship theorem.Combinatorial Mathematics and Its Applications. Proc. Conf. Math. Inst., Oxford D. J. A. Welsh Academic Press New York-Lodon (1971), 307-309. Zbl 0226.05002, MR 0282857
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8Academic Journal
المؤلفون: Stevanović, Dragan
مصطلحات موضوعية: keyword:graphs, keyword:adjacency matrix, keyword:eigenvalues of a graph, keyword:common neighbours, msc:05C50, msc:05C75
وصف الملف: application/pdf
Relation: mr:MR2128363; zbl:Zbl 1110.05064; reference:[1] D. Cvetković, M. Doob, H. Sachs: Spectra of Graphs. Theory and Applications.Johann A. Barth, Heidelberg, 1995. MR 1324340; reference:[2] R. Diestel: Graph Theory.Second edition, Graduate Texts in Mathematics, vol. 173, Springer, New York, 2000. Zbl 0957.05001, MR 1743598; reference:[3] B. Zelinka: Graphs in which each pair of vertices has exactly two common neighbours.Math. Bohem. 118 (1993), 163–165. Zbl 0777.05092, MR 1223481