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: 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

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الاتاحة: http://hdl.handle.net/10338.dmlcz/146971

المؤلفون: Zhang, Guang-Jun, Zhang, Xiao-Dong

مصطلحات موضوعية: keyword:first Dirichlet eigenvalue, keyword:bicyclic graph, keyword:degree sequence, msc:05C35, msc:05C50

وصف الملف: application/pdf

Relation: mr:MR2990185; zbl:Zbl 1265.05429; reference:[1] koğlu, T. Bıyı, Leydold, J.: Faber-Krahn type inequalities for trees.J. Comb. Theory, Ser. B 97 (2007), 159-174. MR 2290318, 10.1016/j.jctb.2006.04.005; reference:[2] Friedman, J.: Some geometric aspects of graphs and their eigenfunctions.Duke Math. J. 69 (1993), 487-525. Zbl 0785.05066, MR 1208809, 10.1215/S0012-7094-93-06921-9; reference:[3] Leydold, J.: The geometry of regular trees with the Faber-Krahn property.Discrete Math. 245 (2002), 155-172. Zbl 0999.05016, MR 1887936, 10.1016/S0012-365X(01)00139-X; reference:[4] Pruss, A. R.: Discrete convolution-rearrangement inequalities and the Faber-Krahn inequality on regular trees.Duke Math. J. 91 (1998), 463-514. Zbl 0943.05056, MR 1604163, 10.1215/S0012-7094-98-09119-0; reference:[5] Zhang, G. J., Zhang, J., Zhang, X. D.: Faber-Krahn Type Inequality for Unicyclic Graphs.Linear and Multilinear Algebra, DOI:10.1080/03081087.2011.651722. 10.1080/03081087.2011.651722; reference:[6] Zhang, X. D.: The Laplacian spectral radii of trees with degree sequences.Discrete Math. 308 (2008), 3143-3150. Zbl 1156.05038, MR 2423396, 10.1016/j.disc.2007.06.017; reference:[7] Zhang, X. D.: The signless Laplacian spectral radius of graphs with given degree sequences.Discrete Appl. Math. 157 (2009), 2928-2937. Zbl 1213.05153, MR 2537494, 10.1016/j.dam.2009.02.022

الاتاحة: http://hdl.handle.net/10338.dmlcz/142837