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Estimation of most effected cycles and busiest network route based on complexity function of graph in fuzzy environment

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A Correction to this article was published on 22 June 2023

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Abstract

Connectivity and strength has a major role in the field of network connecting with real world life. Complexity function is one of these parameter which has manifold number of applications in molecular chemistry and the theory of network. Firstly, this paper introduces the thought of complexity function of fuzzy graph with its properties. Second, based on the highest and lowest load on a network system, the boundaries of complexity function of different types of fuzzy graphs are established. Third, the behavior of complexity function in fuzzy cycle, fuzzy tree and complete fuzzy graph are discussed with their properties. Fourth, applications of these thoughts are bestowed to identify the most effected COVID-19 cycles between some communicated countries using the concept of complexity function of fuzzy graph. Also the selection of the busiest network stations and connected internet paths can be done using the same concept in a graphical wireless network system.

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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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  1. Soumitra Poulik and Ganesh Ghorai have contributed equally to this work.

Authors and Affiliations

  1. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, 721102, West Bengal, 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. Estimation of most effected cycles and busiest network route based on complexity function of graph in fuzzy environment. Artif Intell Rev 55, 4557–4574 (2022). https://doi.org/10.1007/s10462-021-10111-2

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