Fuzzy average edge connectivity with its application to communication networks

Ma, Junye; Lib, Lin; Li, Jing

doi:10.1007/s00500-022-07636-1

Cited by 2 publications

(1 citation statement)

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“…The term complement of FGs was investigated in [17]. The term average connectivity of the classical graphs has been shifted towards fuzzy graphs by Poulik et al [18]. An extension of the FGs named interval-valued fuzzy graphs (IVFGs) was introduced in [19].…”

Section: Introductionmentioning

confidence: 99%

Dominations in bipolar picture fuzzy graphs and social networks

2023

RNA

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In this manuscript, we initiate the concepts of domination in bipolar picture fuzzy graphs (BPPFGs) based on the strong edges. Basically, it is the generalization of both the dominations in bipolar fuzzy graphs (BPFGs) and picture fuzzy graphs (PFGs). In the beginning, we introduce different terms related to the domination of bipolar picture fuzzy graphs (BPPFGs) like vertex cardinality, edge cardinality, strong edge, neighbors, strong neighbor of vertex, private neighborhood, independent sets, dominating sets etc. After this, we provide some important characterizations of domination in bipolar picture fuzzy graphs (BPPFGs) based on minimal dominating sets and maximal independent sets. We also investigate the lower and upper domination numbers of these graphs. Moreover, we discuss the notion of the total domination of bipolar picture fuzzy graphs (BPPFGs) and present few of its properties. In our study, we include the terms status and structurally equivalent of bipolar picture fuzzy graphs (BPPFGs). Finally, we present the application of the domination in bipolar picture fuzzy graphs towards social networking.

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Section: Introductionmentioning

confidence: 99%