论文标题
图形的光谱半径禁止$ C_7 $或$ C_6^{\ triangle} $
Spectral radius of graphs forbidden $C_7$ or $C_6^{\triangle}$
论文作者
论文摘要
令$ c_k^{\ triangle} $是从周期$ c_ {k} $获得的图形，通过在$ c_ {k} $中连接两个相邻顶点的新顶点来获得。在本说明中，我们获得了所有尺寸$ m $的图表中的光谱半径最大化的图形，并且包含$ c_6^{\ triangle} $的任何子图同构。作为副产品，我们将证明，如果光谱半径$λ（g）\ ge1+\ sqrt {m-2} $，则$ g $必须包含所有循环$ c_i $ for $ 3 \ le i \ le 7 $，除非$ g \ g \ g \ g \ cong k_3 \ nabla \ weft（
Let $C_k^{\triangle}$ be the graph obtained from a cycle $C_{k}$ by adding a new vertex connecting two adjacent vertices in $C_{k}$. In this note, we obtain the graph maximizing the spectral radius among all graphs with size $m$ and containing no subgraph isomorphic to $C_6^{\triangle}$. As a byproduct, we will show that if the spectral radius $λ(G)\ge1+\sqrt{m-2}$, then $G$ must contains all the cycles $C_i$ for $3\le i\le 7$ unless $G\cong K_3\nabla \left(\frac{m-3}{3}K_1\right)$.
