2021
DOI: 10.3390/math9172143
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Domination in Fuzzy Directed Graphs

Abstract: A new domination parameter in a fuzzy digraph is proposed to espouse a contribution in the domain of domination in a fuzzy graph and a directed graph. Let GD*=V,A be a directed simple graph, where V is a finite nonempty set and A=x,y:x,y∈V,x≠y. A fuzzy digraph GD=σD,μD is a pair of two functions σD:V→0,1 and μD:A→0,1, such that μDx,y≤σDx∧σDy, where x,y∈V. An edge μDx,y of a fuzzy digraph is called an effective edge if μDx,y=σDx∧σDy. Let x,y∈V. The vertex σDx dominates σDy in GD if μDx,y is an effective edge. L… Show more

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Cited by 13 publications
(10 citation statements)
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“…Since then, it has garnered significant attention in the literature. Following the article by Ernie Cockayne and Stephen Hedetniemi [2], domination in graphs has become a prominent area of study for numerous researchers [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. As researchers continue to delve into this area, we can expect further advancement and insights that will enrich our understanding of graphs.…”
Section: Introductionmentioning
confidence: 99%
“…Since then, it has garnered significant attention in the literature. Following the article by Ernie Cockayne and Stephen Hedetniemi [2], domination in graphs has become a prominent area of study for numerous researchers [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. As researchers continue to delve into this area, we can expect further advancement and insights that will enrich our understanding of graphs.…”
Section: Introductionmentioning
confidence: 99%
“…The domination number 𝛾(𝐺) of a graph 𝐺 is the smallest number of vertices in any minimum dominating set. Numerous types of dominating sets [4][5][6][7][8][9][10][11][12][13][14][15][16] have been discovered since the introduction of domination theory. One type of a dominating set is the inverse dominating set.…”
Section: Introductionmentioning
confidence: 99%
“…The domination numberγ(𝐺) of 𝐺 is the smallest cardinality of a dominating set 𝐷 of 𝐺. There are several studies related to the concept of domination in graphs [3][4][5][6][7][8][9][10][11][12][13][14][15]. One of the parameters of domination in graphs is perfect domination in graphs for which definition was given by Cockayne, et.…”
Section: Introductionmentioning
confidence: 99%