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Application of Bipolar Fuzzy Sets in Graph Structures


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1 Department of Mathematics, University of the Punjab, New Campus, Lahore 54590, Pakistan
 

A graph structure is a useful tool in solving the combinatorial problems in different areas of computer science and computational intelligence systems. In this paper, we apply the concept of bipolar fuzzy sets to graph structures. We introduce certain notions, including bipolar fuzzy graph structure (BFGS), strong bipolar fuzzy graph structure, bipolar fuzzy Ni-cycle, bipolar fuzzy Ni-tree, bipolar fuzzy Ni-cut vertex, and bipolar fuzzy Ni-bridge, and illustrate these notions by several examples. We study Φ-complement, self-complement, strong self-complement, and totally strong self-complement in bipolar fuzzy graph structures, and we investigate some of their interesting properties.
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  • Application of Bipolar Fuzzy Sets in Graph Structures

Abstract Views: 106  |  PDF Views: 16

Authors

Muhammad Akram
Department of Mathematics, University of the Punjab, New Campus, Lahore 54590, Pakistan
Rabia Akmal
Department of Mathematics, University of the Punjab, New Campus, Lahore 54590, Pakistan

Abstract


A graph structure is a useful tool in solving the combinatorial problems in different areas of computer science and computational intelligence systems. In this paper, we apply the concept of bipolar fuzzy sets to graph structures. We introduce certain notions, including bipolar fuzzy graph structure (BFGS), strong bipolar fuzzy graph structure, bipolar fuzzy Ni-cycle, bipolar fuzzy Ni-tree, bipolar fuzzy Ni-cut vertex, and bipolar fuzzy Ni-bridge, and illustrate these notions by several examples. We study Φ-complement, self-complement, strong self-complement, and totally strong self-complement in bipolar fuzzy graph structures, and we investigate some of their interesting properties.