The Signless Dirichlet Spectral Radius of Unicyclic Graphs
Received:January 20, 2016  Revised:February 27, 2017
Key Words: signless Dirichlet spectral radius   unicyclic graph   degree sequence
Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.11271256; 11601208).
 Author Name Affiliation Guangjun ZHANG School of Mathematics and Physics, Qingdao University of Science and Technology, Shandong 266061, P. R. China Weixia LI School of Mathematics and Statistics, Qingdao University, Shandong 266071, P. R. China
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Let $G$ be a simple connected graph with pendant vertex set $\partial V$ and nonpendant vertex set $V_0$. The signless Laplacian matrix of $G$ is denoted by $Q(G)$. The signless Dirichlet eigenvalue is a real number $\lambda$ such that there exists a function $f \neq 0$ on $V(G)$ such that $Q(G)f(u)=\lambda f(u)$ for $u \in V_0$ and $f(u)=0$ for $u \in \partial V$. The signless Dirichlet spectral radius $\lambda(G)$ is the largest signless Dirichlet eigenvalue. In this paper, the unicyclic graphs with the largest signless Dirichlet spectral radius among all unicyclic graphs with a given degree sequence are characterized.