# Strength of strongest dominating sets in fuzzy graphs

Document Type : Original paper

Authors

1 Shahed University

2 Shahrood University of Technology

3 Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, iran

Abstract

A set S of vertices in a graph G=(V,E) is a dominating set of
G if every vertex of V-S is adjacent to some vertex of S.
For an integer k≥1, a set S of vertices is a k-step
dominating set if any vertex of $G$ is at distance k from some
vertex of S. In this paper, using membership
values of vertices and edges in fuzzy graphs, we introduce the concepts of strength of strongest
dominating set as well as strength of strongest
$k$-step dominating set in fuzzy graphs. We determine various bounds for
these parameters in fuzzy graphs. We also determine the strength
of strongest dominating set in some families of fuzzy graphs
including complete fuzzy graphs and complete bipartite fuzzy
graphs.

Keywords

Main Subjects