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Discrete Dynamics in Nature and Society
Volume 2016, Article ID 6301693, 9 pages
http://dx.doi.org/10.1155/2016/6301693
Research Article

Certain Concepts in -Polar Fuzzy Graph Structures

1Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan
2Department of Mathematics, Faculty of Science, King Abdulaziz University, Al-Faisaliah Campus, Jeddah, Saudi Arabia

Received 7 June 2016; Accepted 14 August 2016

Academic Editor: Juan R. Torregrosa

Copyright © 2016 Muhammad Akram et al. 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

We apply the concept of -polar fuzzy sets to graph structures. We introduce certain concepts in -polar fuzzy graph structures, including strong -polar fuzzy graph structure, -polar fuzzy -cycle, -polar fuzzy -tree, -polar fuzzy -cut vertex, and -polar fuzzy -bridge, and we illustrate these concepts by several examples. We present the notions of -complement of an -polar fuzzy graph structure and self-complementary, strong self-complementary, totally strong self-complementary -polar fuzzy graph structures, and we investigate some of their properties.