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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 857070, 11 pages
http://dx.doi.org/10.1155/2013/857070
Research Article

Certain Types of Interval-Valued Fuzzy Graphs

1Punjab University College of Information Technology, University of the Punjab, Old Campus, Lahore 54000, Pakistan
2Department of Mathematics, Faculty of Sciences (Girls), King Abdulaziz University, Jeddah, Saudi Arabia
3Institute of Mathematics and Computer Science, Wroclaw University of Technology, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland

Received 29 July 2013; Accepted 31 August 2013

Academic Editor: Chong Lin

Copyright © 2013 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 propose certain types of interval-valued fuzzy graphs including balanced interval-valued fuzzy graphs, neighbourly irregular interval-valued fuzzy graphs, neighbourly total irregular interval-valued fuzzy graphs, highly irregular interval-valued fuzzy graphs, and highly total irregular interval-valued fuzzy graphs. Some interesting properties associated with these new interval-valued fuzzy graphs are investigated, and necessary and sufficient conditions under which neighbourly irregular and highly irregular interval-valued fuzzy graphs are equivalent are obtained. We also describe the relationship between intuitionistic fuzzy graphs and interval-valued fuzzy graphs.