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Permanental Bounds for the Signless Laplacian Matrix of a Unicyclic Graph with Diameter d

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Abstract

Let \({\fancyscript{U}_{n}}\) be the set of n-vertex unicyclic graphs, \({\fancyscript{U}_n^d}\) be the set of n-vertex unicyclic graphs of diameter d. In this paper we determine the second-minimum value of signless Laplacian permanent of graphs among \({\fancyscript{U}_{n}}\) ; as well we obtain the lower bound for the signless Laplacian permanent of graphs in \({\fancyscript{U}_{n}^d}\) . The corresponding extremal graphs are characterized.

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  1. Faculty of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, People’s Republic of China

    Shuchao Li & Li Zhang

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  1. Shuchao Li
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  2. Li Zhang
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Correspondence to Shuchao Li.

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Li, S., Zhang, L. Permanental Bounds for the Signless Laplacian Matrix of a Unicyclic Graph with Diameter d . Graphs and Combinatorics 28, 531–546 (2012). https://doi.org/10.1007/s00373-011-1057-7

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