Dominations in bipolar picture fuzzy graphs and social networks
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Keywords:
domination in BPPFGs, Upper, lower and total domination numbers of BPPFGs, status of a BPPFG 2010 Mathematics Subject Classification: 03E72, 05C72Abstract
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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