Abstract
AbstractTheoretical concepts of graphs are highly utilized by computer science applications. Especially in research areas of computer science such as data mining, image segmentation, clustering, image capturing and networking. In this paper, we discussed some properties of the µ–complement of bipolar fuzzy graphs. Self µ–complement bipolar fuzzy graphs and self weak µ–complement bipolar fuzzy graphs are defined and a necessary condition for a bipolar fuzzy graph to be self µ–complement is given. We defined busy vertices and free vertices in bipolar fuzzy graphs and studied their image under an isomorphism. Categorical properties of bipolar fuzzy graphs are discussed. Also, we investigated some properties of isomorphism on bipolar fuzzy graphs.
Highlights
Science and technology is featured with complex processes and phenomena for which complete information is not always available
The main objective of this paper is to study of bipolar fuzzy graph and this graph is based on the bipolar fuzzy set defined below
We have introduced some properties of bipolar fuzzy graphs in this paper
Summary
Science and technology is featured with complex processes and phenomena for which complete information is not always available. For such cases, mathematical models are developed to handle various types of systems containing elements of uncertainty. Bipolar fuzzy set is an extension of fuzzy set. In 2011, Akram and Dudek [2] defined regular bipolar fuzzy graphs and introduced the concept of regular and totally regular bipolar fuzzy graphs. Samanta and Pal discussed some properties of bipolar fuzzy graphs in [19,20,21]. We defined μ−complement of bipolar fuzzy graphs and investigated some properties of it. Terminologies and applications not mentioned in the paper, the readers are referred to [23,24,25, 29, 30, 32, 33]
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