Strength of strongest dominating sets in fuzzy graphs


  • Maryam Ghorani Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, iran

A set S of vertices in a graph G=(V,E) is a dominating set ofG 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 somevertex of S. In this paper, using membership values of vertices and edges in fuzzy graphs, we introduce the concepts of strength of strongestdominating set as well as strength of strongest$k$-step dominating set in fuzzy graphs. We determine various bounds forthese parameters in fuzzy graphs. We also determine the strengthof strongest dominating set in some families of fuzzy graphsincluding complete fuzzy graphs and complete bipartite fuzzygraphs.

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عنوان ژورنال:

دوره 6  شماره 2

صفحات  287- 297

تاریخ انتشار 2021-12-01

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