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Keywords = weak and co-weak isomorphisms of bipolar picture fuzzy graphs

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22 pages, 530 KiB  
Article
Bipolar Picture Fuzzy Graphs with Application
by Waheed Ahmad Khan, Babir Ali and Abdelghani Taouti
Symmetry 2021, 13(8), 1427; https://doi.org/10.3390/sym13081427 - 4 Aug 2021
Cited by 20 | Viewed by 4377
Abstract
In this manuscript, we introduce and discuss the term bipolar picture fuzzy graphs along with some of its fundamental characteristics and applications. We also initiate the concepts of complete bipolar picture fuzzy graphs and strong bipolar picture fuzzy graphs. Firstly, we apply different [...] Read more.
In this manuscript, we introduce and discuss the term bipolar picture fuzzy graphs along with some of its fundamental characteristics and applications. We also initiate the concepts of complete bipolar picture fuzzy graphs and strong bipolar picture fuzzy graphs. Firstly, we apply different types of operations to bipolar picture fuzzy graphs and then we introduce various products of bipolar picture fuzzy graphs. Several other terms such as order and size, path, neighbourhood degrees, busy values of vertices and edges of bipolar picture fuzzy graphs are also discussed. These terminologies also lay the foundations for the discussion about the regular bipolar picture fuzzy graphs. Moreover, we also discuss isomorphisms, weak and co-weak isomorphisms and automorphisms of bipolar picture fuzzy graphs. Finally, at the base of bipolar picture fuzzy graph we present the construction of a bipolar picture fuzzy acquaintanceship graph, which would be an important tool to measure the symmetry or asymmetry of acquaintanceship levels of social networks, computer networks etc. Full article
(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications)
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