TOTAL RESTRAINED EDGE MONOPHONIC DOMINATION NUMBER M OF A GRAPH

In this paper the concept of total restrained edge monophonic domination number M of a graph G is introduced. For a connected graph G = (V,E) of order at least two, a total restrained edge monophonic dominating set M of a graph G is a restrained edge monophonic dominating set M such that the subgraph induced by M has no isolated vertices. A total restrained edge monophonic dominating set of cardinality is called a - set of G . It is shown that if pand k are positive integers such that 3≤ k ≤ p there exists a connected graph G of order P such that = k . Also For any positive integers 3 < a < b < c < d , there exists a connected graph G such that me(G) = a, , and = d.