A Set S of vertices in a graph G(V,E) is called dominating set,if every vertex v V id either an element or adjacent to S. vertice Total set if S, total G with no isolated subset the such that In this paper we will find perfect Interval graph. We also out induced subgraph regarding which were splitted.

For a connected graph G = (V, E) of order at least two, subset T minimum total monophonic set S is forcing for if the unique containing . A cardinality S. The number ftm(S) in ftm(G) min{ftm(S)}, where taken over all sets G. We determine bounds it and find certain classes graphs. It shown that every pair a, b positive integers with 0 ≤ < ≥ a+4, there exists such mt(G) b.

It is not possible to determine the total vertex of irregular strength all graphs. This study aims ascertain irregularity in prismatic graph amalgamation for n>=4. Determination done by ascertaining largest lower limit and smallest upper limit. The analyzed based on properties other supporting theorems, while labeling vertices edges graph. Based results this study, obtained, namely (4(P2,n))...

in this paper, we introduce the notions of product vague graph, balanced product vague graph, irregularity and total irregularity of any irregular vague graphs and some results are presented. also, density and balanced irregular vague graphs are discussed and some of their properties are established. finally we give an application of vague digraphs.