TY - JOUR
ID - 14163
TI - Strength of strongest dominating sets in fuzzy graphs
JO - Communications in Combinatorics and Optimization
JA - CCO
LA - en
SN - 2538-2128
AU - Farhadi Jalalvand, Marzieh
AU - Jafari Rad, Nader
AU - Ghorani, Maryam
AD - Shahrood University of Technology
AD - Shahed University
AD - Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, iran
Y1 - 2021
PY - 2021
VL - 6
IS - 2
SP - 287
EP - 297
KW - dominating set
KW - Exact 1-step dominating set
KW - Strongest dominating set in fuzzy graphs
KW - Nordhaus-Gaddum type bound
DO - 10.22049/cco.2021.26988.1174
N2 - 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.
UR - https://comb-opt.azaruniv.ac.ir/article_14163.html
L1 - https://comb-opt.azaruniv.ac.ir/article_14163_39e9cbd30c7e18a6c6c3017a77610dd4.pdf
ER -