论文标题
在给定独立数$α$的双块图的光谱半径上
On the spectral radius of bi-block graphs with given independence number $α$
论文作者
论文摘要
如果其每个块都是完整的两部分图，则将连接的图称为Bi-block图。令$ \ mathcal {b}（\ Mathbf {k}，α）$为$ \ Mathbf {k} $ vertices上的Bi-Block Graph类，具有给定的独立号码$α$。很容易看出每个Biblock图都是两部分图。对于$ \ Mathbf {k} $ vertices上的两分之二图$ g $，独立数$α（g）$满足$ \ ceil*{\ frac {\ frac {\ mathbf {k}}} {2}} {2}} \ leqα（g）\ leq \ leq \ leq \ leq \ mathbf {k} k} -1 $。在本文中，我们证明了所有图中的最大光谱半径$ρ（g）$ in $ \ \ \ m nathcal {b}（\ Mathbf {k}，α）$，用于完整的双位图$ k_ {α，\ Mathbf {k} -a}-α} $。
A connected graph is called a bi-block graph if each of its blocks is a complete bipartite graph. Let $\mathcal{B}(\mathbf{k}, α)$ be the class of bi-block graph on $\mathbf{k}$ vertices with given independence number $α$. It is easy to see that every bi-block graph is a bipartite graph. For a bipartite graph $G$ on $\mathbf{k}$ vertices, the independence number $α(G)$ satisfies $\ceil*{\frac{\mathbf{k}}{2}} \leq α(G) \leq \mathbf{k}-1$. In this article, we prove that the maximum spectral radius $ρ(G)$ among all graphs $G$ in $\mathcal{B}(\mathbf{k}, α)$, is uniquely attained for the complete bipartite graph $K_{α, \mathbf{k}-α}$.
