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Applied Computational Intelligence and Soft Computing
Volume 2016, Article ID 5859080, 13 pages
http://dx.doi.org/10.1155/2016/5859080
Research Article

Application of Bipolar Fuzzy Sets in Graph Structures

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

Received 27 November 2015; Revised 25 December 2015; Accepted 28 December 2015

Academic Editor: Baoding Liu

Copyright © 2016 Muhammad Akram and Rabia Akmal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 -cycle, bipolar fuzzy -tree, bipolar fuzzy -cut vertex, and bipolar fuzzy -bridge, and illustrate these notions by several examples. We study -complement, self-complement, strong self-complement, and totally strong self-complement in bipolar fuzzy graph structures, and we investigate some of their interesting properties.