Connected \(M_2\)-Equicoverable Graphs with Circumference at Most \(5\)

Abstract

A graph \(G\) is called \(H\)-equicoverable if every minimal \(H\)-covering in \(G\) is also a minimum \(H\)-covering in \(G\). In this paper, we give the characterization of connected \(M_2\)-equicoverable graphs with circumference at most \(5\).