The Signless Dirichlet Spectral Radius of Unicyclic Graphs 
Received:January 20, 2016 Revised:February 27, 2017 
Key Word:
signless Dirichlet spectral radius unicyclic graph degree sequence

Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant Nos.11271256; 11601208). 

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Abstract: 
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. 
Citation: 
DOI:10.3770/j.issn:20952651.2017.03.002 
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