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.