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Spectral characterization of multicone graphs

Jianfeng Wang;  Haixing Zhao;  Qiongxiang Huang — 2012

Czechoslovak Mathematical Journal

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,...

The chromatic equivalence class of graph B n - 6 , 1 , 2 ¯

Jianfeng Wang;  Qiongxiang Huang;  Chengfu Ye;  Ruying Liu — 2008

Discussiones Mathematicae Graph Theory

By h(G,x) and P(G,λ) we denote the adjoint polynomial and the chromatic polynomial of graph G, respectively. A new invariant of graph G, which is the fourth character R₄(G), is given in this paper. Using the properties of the adjoint polynomials, the adjoint equivalence class of graph B n - 6 , 1 , 2 is determined, which can be regarded as the continuance of the paper written by Wang et al. [J. Wang, R. Liu, C. Ye and Q. Huang, A complete solution to the chromatic equivalence class of graph B n - 7 , 1 , 3 ¯ , Discrete Math....

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