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The spread of unicyclic graphs with given size of maximum matchings

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Abstract

The spread s(G) of a graph G is defined as s(G) = maxi,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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Authors and Affiliations

  1. Center for Combinatorics and LPMC, Nankai University, Tianjin, 300071, P.R. China

    Xueliang Li & Jianbin Zhang

  2. Department of Mathematics, South China Normal University, Guangzhou, 510631, P.R. China

    Bo Zhou

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  1. Xueliang Li
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  2. Jianbin Zhang
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  3. Bo Zhou
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Correspondence to Xueliang Li.

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Li, X., Zhang, J. & Zhou, B. The spread of unicyclic graphs with given size of maximum matchings. J Math Chem 42, 775–788 (2007). https://doi.org/10.1007/s10910-006-9141-6

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  • DOI: https://doi.org/10.1007/s10910-006-9141-6

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