Geodesic
Spectral characterization of multicone graphs
Czechoslovak Mathematical Journal, Tome 62 (2012) no. 1, pp. 117-126
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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.
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.
DOI : 10.1007/s10587-012-0021-x
Classification : 05C50
Keywords: adjacency matrix; cospectral graph; spectral characteriztion; multicone graph 
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Wang, Jianfeng; Zhao, Haixing; Huang, Qiongxiang. Spectral characterization of multicone graphs. Czechoslovak Mathematical Journal, Tome 62 (2012) no. 1, pp. 117-126. doi: 10.1007/s10587-012-0021-x

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