文摘
A graph G is called H-equicoverable if every minimal H-covering in G is also a minimum H-covering in G. All \(P_{3}\)-equicoverable graphs were characterized in Zhang (Discret Appl Math 156:647–661, 2008). In 2011, connected \(M_2\)-equicoverable graphs that contains cycles were characterized [see Zhang and Jiang (J Tianjin Univ:44:466–470, 2011) and Zhang and Zhang (Ars Comb 101:45–63, 2011)]. In this paper, we give the characterization of all disconnected \(M_{2}\)-equicoverable graphs and all \(M_{2}\)-equicoverable trees. So all \(M_2\)-equicoverable graphs are characterized now.