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Fuzzy fractional coloring of fuzzy graph with its application

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Abstract

In this article, a new idea of fuzzy fractional coloring of fuzzy graph is presented and fuzzy fractional chromatic number is defined. A relationship between fuzzy fractional chromatic number and fuzzy fractional clique number is established. Some properties of fuzzy chromatic number of fuzzy graphs and fuzzy fractional chromatic number of fuzzy graphs are proved and the concept of k-strong adjacent vertices is introduced. Fuzzy chromatic number and fuzzy fractional chromatic number have been calculated on lexicographic product of two fuzzy graphs. Also, fuzzy chromatic number, independence number and fuzzy fractional chromatic number have been investigated on disjoint union of two fuzzy graphs. Lastly, a real life application of fuzzy fractional coloring on fuzzy graph is discussed.

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Acknowledgements

The authors are highly grateful to the learned reviewers for their valuable comments and suggestions to improve the quality of the article. Financial support of first author offered by University Grants commission, New Delhi, India (UGC Ref.No:1215/CSIR-UGC NET DEC.2016) is thankfully acknowledged.

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Authors and Affiliations

  1. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, 721102, India

    Tanmoy Mahapatra, Ganesh Ghorai & Madhumangal Pal

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  1. Tanmoy Mahapatra
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  2. Ganesh Ghorai
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  3. Madhumangal Pal
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Correspondence to Ganesh Ghorai.

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Mahapatra, T., Ghorai, G. & Pal, M. Fuzzy fractional coloring of fuzzy graph with its application. J Ambient Intell Human Comput 11, 5771–5784 (2020). https://doi.org/10.1007/s12652-020-01953-9

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