Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
adjacency matrix; cospectral graph; spectral characteriztion; multicone graph
adjacency matrix; cospectral graph; spectral characteriztion; multicone graph
Summary:
A multicone graph is defined to be the join of a clique and a regular graph. Based on Zhou and Cho's result [B. Zhou, H. H. Cho, Remarks on spectral radius and Laplacian eigenvalues of a graph, Czech. Math. J. 55 (130) (2005), 781–790], the spectral characterization of multicone graphs is investigated. Particularly, we determine a necessary and sufficient condition for two multicone graphs to be cospectral graphs and investigate the structures of graphs cospectral to a multicone graph. Additionally, lower and upper bounds for the largest eigenvalue of a multicone graph are given.
References:
[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
[2] Cvetković, D., Doob, M., Simić, S.: Generalized line graphs. J. Graph Theory 5 (1981), 385-399. DOI 10.1002/jgt.3190050408 | MR 0635701 | Zbl 0475.05061
[3] Dam, E. R. van, Haemers, W. H.: Which graphs are determined by their spectrum?. Linear Algebra Appl. 373 (2003), 241-272. MR 2022290
[4] Dam, E. R. van, Haemers, W. H.: Developments on spectral characterizations of graphs. Discrete Math. 309 (2009), 576-586. DOI 10.1016/j.disc.2008.08.019 | MR 2499010
[5] Godsil, C. D., McKay, B. D.: Constructing cospectral graphs. Aequationes Math. 25 (1982), 257-268. DOI 10.1007/BF02189621 | MR 0730486 | Zbl 0527.05051
[6] Erdős, P., Rényi, A., Sós, V. T.: On a problem of graph theory. Stud. Sci. Math. Hung. 1 (1966), 215-235. MR 0223262
[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. DOI 10.1002/hlca.19560390623
[8] Haemers, W. H., Spence, E.: Enumeration of cospectral graphs. Eur. J. Comb. 25 (2004), 199-211. DOI 10.1016/S0195-6698(03)00100-8 | MR 2070541 | Zbl 1033.05070
[9] Harary, F., King, C., Mowshowitz, A., Read, R.: Cospectral graphs and digraphs. Bull. Lond. Math. Soc. 3 (1971), 321-328. DOI 10.1112/blms/3.3.321 | MR 0294176 | Zbl 0224.05125
[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. DOI 10.1006/jctb.2000.1997 | MR 1814902 | Zbl 1024.05059
[11] Johnson, C. R., Newman, M.: A note on cospectral graphs. J. Comb. Theory, Ser. B 28 (1980), 96-103. DOI 10.1016/0095-8956(80)90058-1 | MR 0565513 | Zbl 0431.05021
[12] Nikiforov, V.: Some inequalities for the largest eigenvalue of a graph. Comb. Probab. Comput. 11 (2002), 179-189. DOI 10.1017/S0963548301004928 | MR 1888908 | Zbl 1005.05029
[13] Zhou, B., Cho, H. H.: Remarks on spectral radius and Laplacian eigenvalues of a graph. Czech. Math. J. 55 (130) (2005), 781-790. DOI 10.1007/s10587-005-0064-3 | MR 2153101 | Zbl 1081.05068
[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. DOI 10.1016/j.disc.2010.06.030 | MR 2677645 | Zbl 1208.05079
[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. MR 0282857 | Zbl 0226.05002
Search
Partner of
