Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 6 2 2021 12 01 Strength of strongest dominating sets in fuzzy graphs 287 297 14163 10.22049/cco.2021.26988.1174 EN Marzieh Farhadi Jalalvand Shahrood University of Technology Nader Jafari Rad Shahed University Maryam Ghorani Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, iran Journal Article 2020 10 30 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.

https://comb-opt.azaruniv.ac.ir/article_14163_39e9cbd30c7e18a6c6c3017a77610dd4.pdf