Maximizing algebraic connectivity for quasi-tree graphs with given matching number

Abstract

A connected graph $G=(V,E)$ is called a quasi-tree graph if there exists a vertex $v_0\in V(G)$ such that $G–v_0$ is a tree. In this paper, we determine the largest algebraic connectivity together with the corresponding extremal graphs among all quasi-tree graphs of order $n$ with a given matching number.