单圈图的无符号狄利克雷谱半径

The Signless Dirichlet Spectral Radius of Unicyclic Graphs

中文关键词:  无符号狄利克雷谱半径  单圈图  度序列

英文关键词:signless Dirichlet spectral radius  unicyclic graph  degree sequence

中文摘要:

      设$G$是一个具有悬挂点集合$\partial V$和非悬挂点集合$V_0$的简单连通图. $Q(G)$表示$G$的无符号拉普拉斯矩阵. 如果存在$V(G)$上的非零函数$f$使得实数$\lambda$满足当$u \in V_0$ 时,有$Q(G)f(u)=\lambda f(u)$,并且当$u \in \partial V$时,有$f(u)=0$,我们就称$\lambda$为$G$的无符号狄利克雷特征值.其中,最大的无符号狄利克雷特征值被称为无符号狄利克雷谱半径.本文刻画了在具有相同度序列的单圈图中具有最大无符号狄利克雷谱半径的图.

英文摘要:

      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.