The Signless Laplacian Spectral Characterization of Strongly Connected Bicyclic Digraphs
Received:December 11, 2014  Revised:May 27, 2015
Key Words: the signless Laplacian spectral radius   $\infty$-digraph   $\theta$-digraphn   bicyclic digraph  
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11171273).
Author NameAffiliation
Weige XI Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Shaanxi 710072, P. R. China 
Ligong WANG Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Shaanxi 710072, P. R. China 
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Abstract:
      Let $\overrightarrow{G}$ be a digraph and $A(\overrightarrow{G})$ be the adjacency matrix of $\overrightarrow{G}$. Let $D(\overrightarrow{G})$ be the diagonal matrix with outdegrees of vertices of $\overrightarrow{G}$ and $Q(\overrightarrow{G})=D(\overrightarrow{G})+A(\overrightarrow{G})$ be the signless Laplacian matrix of $\overrightarrow{G}$. The spectral radius of $Q(\overrightarrow{G})$ is called the signless Laplacian spectral radius of $\overrightarrow{G}$. In this paper, we determine the unique digraph which attains the maximum (or minimum) signless Laplacian spectral radius among all strongly connected bicyclic digraphs. Furthermore, we prove that any strongly connected bicyclic digraph is determined by the signless Laplacian spectrum.
Citation:
DOI:10.3770/j.issn:2095-2651.2016.01.001
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