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Strength of strongest dominating sets in fuzzy graphs | ||
| Communications in Combinatorics and Optimization | ||
| دوره 6، شماره 2، اسفند 2021، صفحه 287-297 اصل مقاله (380.73 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2021.26988.1174 | ||
| نویسندگان | ||
| Marzieh Farhadi Jalalvand1؛ Nader Jafari Rad* 2؛ Maryam Ghorani3 | ||
| 1Shahrood University of Technology | ||
| 2Shahed University | ||
| 3Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Dominating set؛ Exact 1-step dominating set؛ Strongest dominating set in fuzzy graphs؛ Nordhaus-Gaddum type bound | ||
| مراجع | ||
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