Mathematics

CLC number: O157.5

The A_α-Spectral Radius and k-Extendability in Graphs

图的A_α-谱半径与k-可扩展性

Institute of Applied Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China

^† Corresponding author. E-mail: wenfei@lzjtu.edu.cn

Received: 19 May 2024

Abstract

A graph is called $k$-extendable if each $k$-matching can be extended to a perfect matching. In this paper, we provide a sufficient condition in terms of the ${\mathit{A}}_{\alpha }$-spectral radius for the $k$-extendability of a connected graph and characterize the corresponding extremal graphs. In addition, such an ${\mathit{A}}_{\alpha }$-spectral condition of a connected balanced bipartite graph is also considered, and the corresponding extremal graphs are determined.

摘要

若一个图的任意$k$-匹配都可扩展为该图的完美匹配，则称此图为$k$-可扩展图。本文给出了连通图具有$k$-可扩展性的一个${\mathit{A}}_{\alpha }$-谱条件，并刻画了相应的极图。此外，还考虑了连通平衡二部图具有$k$-可扩展性的一个${\mathit{A}}_{\alpha }$-谱条件及其相应的极图。