On The Study of Edge Monophonic Vertex Covering Number

Abstract

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

Keywords

• monophonic set
• edge monophonic set
• vertex covering set
• edge monophonic vertex cover
• edge monophonic vertex covering number
• etc.