Strongest Exact 1-Step Dominating Set for Fuzzy Graphs

Two vertices in a graph are said to dominate each others if they are adjacent. A set S of vertices in a graph G is a dominating set of G if every vertex is dominated by some vertex of S and exact 1-step dominating set in a graph G is a subset S of vertices of G such that | N(v) ∩ S | = 1 for every v  V(G). A graph is an exact 1-step domination graph if it contains an exact 1- step dominating set. In this paper, we determine strongest dominating set as optimized dominating set in fuzzy graph G and then study its strength andobtain these strengths for fuzzy complete graphs and fuzzy complete bipartite graphs.Then, we define exact 1-Step dominating sets in fuzzy graphs and determine strongest exact 1-Step dominating set for fuzzy graph G. Finally, we obtain new upper bound on the size of exact 1- step domination fuzzy graphs.

کلیدواژه ها:

Dominating Set ، Exact 1-Step Dominating Set ، Strongest Dominating Set ، Strongest Exact 1-Step Dominating Set ، Exact 1- Step Dominating Graph.