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Characterization of regular bipolar fuzzy graphs

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Abstract

In this paper, adjacency sequence of a vertex, first and second fundamental sequences are defined in a bipolar fuzzy graph with example. Some examples are constructed to show that if G is a regular bipolar fuzzy graph (BFG), the underlying crisp graph need not be regular and all the vertices need not have the same adjacency sequence. Also it is shown that if G and its underlying crisp graph are regular, all the vertices need not have the same adjacency sequence. A necessary and sufficient condition is established for a BFG with at most four vertices to be regular using the concept of adjacency sequences. Moreover, some characterizations have been made for a line graph of a regular BFG to be regular, the complement of a regular BFG to be regular, etc.

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Acknowledgements

The authors are highly grateful to the Editor and the learned reviewers for their valuable comments and suggestions to improve the quality of the article.

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  1. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, 721 102, India

    Ganesh Ghorai

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  1. Ganesh Ghorai
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Ghorai, G. Characterization of regular bipolar fuzzy graphs. Afr. Mat. 32, 1043–1057 (2021). https://doi.org/10.1007/s13370-021-00880-y

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