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Randic index of bipolar fuzzy graphs and its application in network systems

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Abstract

Connectivity can be used to measure the strength and combined power of a connected network system. Randic index of graph is one such parameter and it can measure the total combined power of a connected graphical transmission system. For two opposite sided opinion of vertices as well as edges in a bipolar fuzzy graph, it can measure the uncertainty of vertices and edges along positive and negative sides. In this article, the Randic index of bipolar fuzzy graph and bipolar fuzzy subgraph are introduced with their properties. The upper and lower boundaries of Randic index of bipolar fuzzy graphs are studied with some isomorphic properties. Randic index of directed bipolar fuzzy graphs are introduced. Several formula’s are presented to calculate the Randic index of different types of regular bipolar fuzzy graphs and bipolar fuzzy cycles. Finally, two real life applications of Randic index in bipolar fuzzy graphs are described.

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Acknowledgements

The authors would like to express their sincere gratitude to the anonymous referees for valuable suggestions, which led to great deal of improvement of the original manuscript. The first author is thankful to the Department of Higher Education, Science and Technology and Biotechnology, Government of West Bengal, India, for the award of Swami Vivekananda merit-cum-means scholarship (Award No. 52-Edn (B)/5B-15/2017 dated 07/06/2017) to meet up the financial expenditure to carry out the research work. The third author acknowledges the support of DST-FIST, New Delhi (India) (Sanction No. SR/FST/MS- I/2018/21) for carrying out this work.

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Authors and Affiliations

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

    Soumitra Poulik, Sankar Das & Ganesh Ghorai

  2. Department of Mathematics, Kharagpur College, Kharagpur, 721 305, India

    Sankar Das

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  1. Soumitra Poulik
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  2. Sankar Das
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Correspondence to Ganesh Ghorai.

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Poulik, S., Das, S. & Ghorai, G. Randic index of bipolar fuzzy graphs and its application in network systems. J. Appl. Math. Comput. 68, 2317–2341 (2022). https://doi.org/10.1007/s12190-021-01619-5

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