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On nested split graphs whose second largest eigenvalue is less than 1. (English) Zbl 1194.05098
Summary: We determine all nested split graphs (i.e. graphs having no induced subgraphs equal to 2K 2 ,P 4 or C 4 ) having the second largest eigenvalue less than 1 and give some data and observations regarding obtained results.
05C50Graphs and linear algebra
[1]T. Bıyıkogbreve;lu, S.K. Simić, Z. Stanić, Some notes on spectra of cographs, Ars Combin., in press.
[2]Corneil, D. G.; Perl, Y.; Stewart, L. K.: A linear recognition algorithm for cographs, SIAM J. Comput. 14, 926-934 (1985) · Zbl 0575.68065 · doi:10.1137/0214065
[3]Cvetković, D.: On graphs whose second largest eigenvalue does not exceed 1, Publ. inst. Math. 31, No. 45, 15-20 (1982) · Zbl 0522.05044
[4]Cvetković, D.; Doob, M.; Sachs, H.: Spectra of graphs – theory and application, (1995)
[5]Cvetković, D.; Rowlinson, P.; Simić, S.: Eigenspaces of graphs, (1997) · Zbl 0878.05057
[6]Cvetković, D.; Rowlinson, P.; Simić, S.: Spectral generalizations of line graphs – on line graphs with least eigenvalue -2, London math. Soc., lecture notes series 314 (2004)
[7]Guo, Shu-Guang: On bicyclic graphs whose second largest eigenvalue does not exceed 1, Linear algebra appl. 407, 201-210 (2005) · Zbl 1073.05043 · doi:10.1016/j.laa.2005.05.010
[8]M. Petrović, Z. Radosavljević, Spectrally constrained graphs, Faculty of Science, Kragujevac, Yugoslavia, 2001.
[9]G.F. Royle, The rank of cographs, Electron. J. Comb. 10 (1), Research paper N11:7 p., 2003.
[10]Simić, S. K.; Marzi, E. M. Li; Belardo, F.: Connected graphs of fixed order and size with maximal index: structural considerations, Le matematiche 59, 349-365 (2004) · Zbl 1195.05045
[11]Stanić, Z.: On graphs whose second largest eigenvalue equals 1 – the star complement technique, Linear algebra appl. 420, 700-710 (2007) · Zbl 1106.05067 · doi:10.1016/j.laa.2006.08.025
[12]Stanić, Z.: On regular graphs and coronas whose second largest eigenvalue does not exceed 1, Linear and multilinear algebra (2008)
[13]Z. Stanić, S.K. Simić, On graphs with unicyclic star complement for 1 as the second largest eigenvalue, in: N. Bokan, M. Djorić, A.T. Fomenko, Z. Rakić, B. Wegner, J. Wess (Eds.), Proceedings of the Conference Contemporary Geometry and Related Topics, Belgrade, June 26 – July 2, 2005, Faculty of Mathematics, Belgrade, 2006, pp. 475 – 484. · Zbl 1142.05054
[14]Xu, Guang-Hui: On unicyclic graphs whose second largest eigenvalue does not exceed 1, Discrete appl. Math. 136, 117-124 (2004) · Zbl 1032.05085 · doi:10.1016/S0166-218X(03)00203-8