Bipolar Fuzzy Trees

Year 2016, Volume: 4 Issue: 3, 58 - 72, 30.09.2016

Muhammad Akram Adeel Farooq

Abstract

Connectivity has an important role in different
disciplines of computer science including computer network. In the design of a
network, it is important to analyze connections by the levels. The structural
properties of bipolar fuzzy graphs provide a tool that allows for the solution
of operations research problems. In this paper, we introduce various types of
bipolar fuzzy bridges, bipolar fuzzy cut-vertices, bipolar fuzzy cycles and
bipolar fuzzy trees in bipolar fuzzy graphs, and investigate some of their
properties. Most of these various types are defined in terms of levels. We also
describe comparison of these types.

Keywords

Bipolar fuzzy cycles, bipolar fuzzy trees, bipolar fuzzy bridges, and bipolar fuzzy cut-vertices

References

• M. Akram, Bipolar fuzzy graphs, Information Sciences 181 (2011) 5548-5564.
• M. Akram, Bipolar fuzzy graphs with applications, Knowledge Based Systems, 39(2013) 1-8.
• M. Akram and W.A. Dudek, Regular bipolar fuzzy graphs, Neural Computing & Applications 21(2012)197-205.
• M. Akram and M.G. Karunambigai, Metric in bipolar fuzzy graphs, World Applied Sciences Journal 14(2011)1920-1927.
• M. Akram, S. Li and K. P. Shum, Antipodal bipolar fuzzy graphs, Italian Journal of Pure and Applied Mathematics, 31(2013)425-438.
• M. Akram, W.A. Dudek and S. Sarwar, Properties of bipolar fuzzy hypergraphs, Italian Journal of Pure and Applied Mathematics, 31(2013)426-458.
• P. Bhattacharya, Some remarks on fuzzy graphs, Pattern Recognition Letter 6(1987), 297-302.
• K.R. Bhutani and A. Rosenfeld, Strong arcs in fuzzy graphs, Information Sciences 152 (2003)319-322.
• A. Kauffman, Introduction a la Theorie des Sous-emsembles Flous, Masson et Cie, Vol.1, 1973.
• L.T. Koczy, ıFuzzy graphs in the evaluation and optimization of networks, Fuzzy sets and systems, 46 (3)(1992) 307-319.
• S. Mathew and M.S. Sunitha, Types of arcs in a fuzzy graph, Information Sciences 179(11)(2009) 1760-1768.
• K.-M. Lee, Bipolar-valued fuzzy sets and their basic operations, Proc. Int. Conf., Bangkok, Thailand, (2000) 307-317.
• J.N. Mordeson and P.S. Nair, Fuzzy graphs and fuzzy hypergraphs, Physica Verlag, Heidelberg 1998; Second Edition 2001.
• A. Nagoorgani and V.T. Chandrasekaran A first look at fuzzy graph theory, Allied Publishers Pvt. Ltd, 2010.
• A. Rosenfeld, Fuzzy graphs, Fuzzy Sets and their Applications (L.A. Zadeh, K.S. Fu, M. Shimura, Eds.), Academic Press, New York (1975) 77-95.
• M.S. Sunitha and A. Vijayakumar, A characterization of fuzzy trees, Information Sciences 113 (1999) 293-300.
• A. Rosenfeld, Fuzzy graphs, Fuzzy Sets and their Applications (L.A. Zadeh, K.S. Fu, M. Shimura, Eds.), Academic Press, New York (1975) 77-95.
• M.S. Sunitha and A. Vijayakumar, Complement of a fuzzy graph, Indian J. Pure Appl. Math. 33(2002) 1451-1464.
• L.A. Zadeh, Fuzzy sets, Information and Control 8(1965) 338-353.
• L.A. Zadeh, Similarity relations and fuzzy orderings, Information Sciences 3(2)(1971) 177-200.
• W.-R. Zhang, Bipolar fuzzy sets and relations: a computational framework forcognitive modeling and multiagent decision analysis, Proc. of IEEE Conf. (1994) 305-309.
• [22] W.-R. Zhang, Bipolar fuzzy sets, Proc. of FUZZ-IEEE (1998) 835-840.