Spectral radius and maximum matching covered graphs with bounded matching number

Abstract

Let $G$ be a graph. The {\em spectral radius} of $G$ is the largest eigenvalue of its {\em adjacency matrix}. A {\em matching} of $G$ is a set of disjoint edges of $G$. The {\em matching number} of $G$ is the size of a maximum matching (i.e., a matching with maximum edges). The graph $G$ is called {\em maximum matching covered} if each edge of $G$ is contained in a maximum matching. In this paper, we give a sharp spectral radius condition for graphs with bounded matching number to be maximum matching covered.