On the spectral radii and the signless Laplacian spectral radii of c-cyclic graphs with fixed maximum degree |
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Authors: | Muhuo Liu Bolian Liu |
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Institution: | a Department of Applied Mathematics, South China Agricultural University, Guangzhou 510642, PR China b School of Mathematic Science, South China Normal University, Guangzhou 510631, PR China |
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Abstract: | If G is a connected undirected simple graph on n vertices and n+c-1 edges, then G is called a c-cyclic graph. Specially, G is called a tricyclic graph if c=3. Let Δ(G) be the maximum degree of G. In this paper, we determine the structural characterizations of the c-cyclic graphs, which have the maximum spectral radii (resp. signless Laplacian spectral radii) in the class of c-cyclic graphs on n vertices with fixed maximum degree . Moreover, we prove that the spectral radius of a tricyclic graph G strictly increases with its maximum degree when , and identify the first six largest spectral radii and the corresponding graphs in the class of tricyclic graphs on n vertices. |
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Keywords: | 05C35 15A48 05C50 |
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