图的独立数、本质连通度与距离谱半径
Independence number, essential connectivity and the distance spectral radius of graphs
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中文总结 AI 辅助
本文研究图的独立数与本质连通度对距离谱半径的影响，确定了给定独立数和本质连通度下达到最小距离谱半径的n阶连通图，并完整刻画了极图结构。
中文摘要 AI 辅助
图G的一个独立集是VG的一个子集，其中任意两个顶点都不相邻。图G中最大独立集的基数称为G的独立数，记为α(G)。图G的本质连通度κ'(G)定义为移除后产生一个具有至少两个非平凡连通分支的不连通图所需的最少顶点数。本文确定了在给定独立数和本质连通度条件下，达到最小距离谱半径的n阶连通图，并完整刻画了相应的极图。
英文摘要
An independent set of a graph G is a subset of VG, no two of which are adjacent. The cardinality of a maximum independent set in a graph G is called the independence number of G, denoted by alpha(G). The essential connectivity kappa'(G) of a graph G is denoted as the minimum number of vertices of G whose removal produces a disconnected graph with at least two non-trivial components. In this paper, we determine the n-vertex connected graphs with given independence number and essential connectivity that attain the minimum distance spectral radius, and fully characterize the corresponding extremal graphs.
发表机构
- College of Mathematics and System Science, Xinjiang University（新疆大学数学与系统科学学院）
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