具有最小邻接谱隙的连通图

中文摘要 AI 辅助

设$G$为连通图，$\u03bb_1(G) > \u03bb_2(G)$表示其两个最大的邻接特征值。$G$的谱隙定义为差值$\u03bb_1(G) - \u03bb_2(G)$。对于整数$r\geq 2$和$s\geq 0$，双风筝图$DK(r,s)$由两个顶点不相交的完全图$K_r$的副本构成，并将每个团的一个指定顶点连接到一条具有$s$个内部顶点的路径上。Stanić（2013）猜想每个具有最小邻接谱隙的$n$顶点连通图都是双风筝图。在本文中，我们证实了对于足够大的$n$，该猜想成立。

英文摘要

Let $G$ be a connected graph, and let $λ_1(G) > λ_2(G)$ denote its two largest adjacency eigenvalues. The spectral gap of $G$ is defined as the difference $λ_1(G) - λ_2(G)$. For integers $r\geq 2$ and $s\geq 0$, the double kite $DK(r,s)$ is formed by taking two vertex-disjoint copies of the complete graph $K_r$ and joining one specified vertex of each clique to a path with $s$ internal vertices. Stanić (2013) conjectured that every connected $n$-vertex graph with minimum adjacency spectral gap is a double kite. In this paper, we confirm this conjecture for sufficiently large $n$.

发表机构

• School of Mathematical Sciences, Anhui University（安徽大学数学科学学院）
• Department of Mathematics & Statistics, Villanova University（维拉诺瓦大学数学与统计系）

机构由 AI 辅助整理，请以论文原文为准。