| Title:
|
Spectral characterization of multicone graphs (English) |
| Author:
|
Wang, Jianfeng |
| Author:
|
Zhao, Haixing |
| Author:
|
Huang, Qiongxiang |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
62 |
| Issue:
|
1 |
| Year:
|
2012 |
| Pages:
|
117-126 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
adjacency matrix |
| Keyword:
|
cospectral graph |
| Keyword:
|
spectral characteriztion |
| Keyword:
|
multicone graph |
| MSC:
|
05C50 |
| idZBL:
|
Zbl 1249.05256 |
| idMR:
|
MR2899739 |
| DOI:
|
10.1007/s10587-012-0021-x |
| . |
| Date available:
|
2012-03-05T07:16:48Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142045 |
| . |
| 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 |
| . |
