For a connected graph G of order n ≥ 2, a set S of vertices of G, is monophonic vertex cover of G if S is both a monophonic set and a vertex cover of G. The minimum cardinality of a monophonic vertex cover of G is called the monophonic vertex covering number of G and is denoted by m_α (G). Any monophonic vertex cover of cardinality m_α (G) is a m_α-set of G. Some general properties satisfied by monophonic vertex cover are studied. The monophonic vertex covering number of several classes of graphs are determined.

monophonic set, vertex covering set, monophonic vertex cover, monophonic vertex covering number.