The spread of unicyclic graphs with given size of maximum matchings |
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Authors: | Xueliang Li Jianbin Zhang Bo Zhou |
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Institution: | (1) Center for Combinatorics and LPMC, Nankai University, Tianjin, 300071, P.R. China;(2) Department of Mathematics, South China Normal University, Guangzhou, 510631, P.R. China |
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Abstract: | The spread s(G) of a graph G is defined as s(G) = max
i,j
|λ
i
− λ
j
|, where the maximum is taken over all pairs of eigenvalues of G. Let U(n,k) denote the set of all unicyclic graphs on n vertices with a maximum matching of cardinality k, and U
*(n,k) the set of triangle-free graphs in U(n,k). In this paper, we determine the graphs with the largest and second largest spectral radius in U
*(n,k), and the graph with the largest spread in U(n,k).
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Keywords: | spread unicyclic graph characteristic polynomial eigenvalue |
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