• M.Little Flower
• P.Arul Paul Sudhahar

In this paper the concept of restrained edge detour monophonic domination number M of a graph G is introduced. For a connected graph G =(V,E) of order at least two, a restrained edge detour monophonic dominating set M of a graph G is a edge detour monophonic dominating set such that either M = V or the sub graph induced by V – M has no isolated vertices. The minimum cardinality of a restrained edge detour monophonic dominating set of G is the restrained edge detour monophonic domination number of G and is denoted by γ_(〖edm〗_r ) (G). We determine bounds for it and characterize graphs which realize these bounds. It is shown that for any two integers p and q with 2 ≤p ≤ q there is a connected graph G such that m(G) = p and γ_em (G) =γ_edm (G)= γ_(〖edm〗_r ) (G) = q. If any two positive integers p and q such that 2≤p≤q thereexists a connected graph G such that γ_m (G) =γ_em (G)=p and γ_edm (G)= γ_(〖edm〗_r ) (G) = q. If any three positive integers p,q and r with 2<p<q<r thereexists a connected graph G such that m(G)=p,em(G)=q and γ_edm (G)= γ_(〖edm〗_r ) (G) = r. If any two positive integers p and q there is a connected graph G such that γ(G)= p and edm(G)=q with γ_edm (G)= γ_(〖edm〗_r ) (G) = p+q-1.

Edge detour monophonic set, Edge detour monophonic number, edge detour monophonic dominating set, edge detour monophonic domination number, restrained edge detour monophonic dominating set and restrained edge detour monophonic domination number.

"RESTRAINED EDGE DETOUR MONOPHONIC DOMINATION NUMBER OF A GRAPH", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.6, Issue 3, page no.786-794, March-2019, Available :http://www.jetir.org/papers/JETIR1903217.pdf

"RESTRAINED EDGE DETOUR MONOPHONIC DOMINATION NUMBER OF A GRAPH", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.6, Issue 3, page no. pp786-794, March-2019, Available at : http://www.jetir.org/papers/JETIR1903217.pdf