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Certain indices of graphs under bipolar fuzzy environment with applications

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Abstract

Connectivity index of graph plays a significant role in chemistry, pharmacology, etc. This paper brings in connectivity index of a bipolar fuzzy graph (BFG) with its boundedness. We examine the changes of connectivity index for a BFG when a vertex or an edge is removed. Some theorems related to these are established. The parameter, average connectivity index of a BFG, is introduced with some theorems. Some special types of nodes like bipolar fuzzy connectivity-enhancing node, bipolar fuzzy connectivity-reducing node, bipolar fuzzy connectivity-neutral node with their properties are introduced. Keeping in mind bipolar judgemental thinking, two applications of these thoughts are bestowed to increase the popularity of women football league in India and another is to determine the order of the places to build colleges in a town.

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Acknowledgements

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 authors are grateful to 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

    Soumitra Poulik & Ganesh Ghorai

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

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Poulik, S., Ghorai, G. Certain indices of graphs under bipolar fuzzy environment with applications. Soft Comput 24, 5119–5131 (2020). https://doi.org/10.1007/s00500-019-04265-z

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