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Further development of F-index for fuzzy graph and its application in Indian railway crime
From the mid-nineteenth century, the railway network has been the most important mode of conveying people and goods in India. 22.15 million passengers used this network and 3.32 million metric tons of goods were also shipped daily from 2019 to 2020. The national rail network comprised 126,366 km of...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer Berlin Heidelberg
2022
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9116720/ https://www.ncbi.nlm.nih.gov/pubmed/35607521 http://dx.doi.org/10.1007/s12190-022-01748-5 |
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author | Islam, Sk Rabiul Pal, Madhumangal |
author_facet | Islam, Sk Rabiul Pal, Madhumangal |
author_sort | Islam, Sk Rabiul |
collection | PubMed |
description | From the mid-nineteenth century, the railway network has been the most important mode of conveying people and goods in India. 22.15 million passengers used this network and 3.32 million metric tons of goods were also shipped daily from 2019 to 2020. The national rail network comprised 126,366 km of track over a route of 67,368 km and 7,325 stations. It is the fourth-largest national railway network globally after the United States, Russia and China. But with the passage, they pose a threat to the general public while travelling, being the instances of crimes rising fourfold in rails. The ongoing railway crime has become a cause of concern for the common passenger now. In this article, F-index for fuzzy graphs is used to analyze the railway crimes in India and compared with three other topological indices. F-index for fuzzy graphs and the first Zagreb index for fuzzy graphs provide similar results whereas F-index for fuzzy graphs provides better realistic results than F-index for crisp graphs and first Zagreb index for crisp graphs to detect the crime in Indian railway. Also, this index is studied for several operations such as Cartesian product, composition, union and join of two fuzzy graphs. Some interesting relations of F-index are established during fuzzy graph transformations. Using those transformation, it is shown that n-vertex star has maximum F-index among the n-vertex trees. Also, maximal n-vertex unicyclic fuzzy graph having r cycle is determined with respect to F-index. |
format | Online Article Text |
id | pubmed-9116720 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | Springer Berlin Heidelberg |
record_format | MEDLINE/PubMed |
spelling | pubmed-91167202022-05-19 Further development of F-index for fuzzy graph and its application in Indian railway crime Islam, Sk Rabiul Pal, Madhumangal J Appl Math Comput Original Research From the mid-nineteenth century, the railway network has been the most important mode of conveying people and goods in India. 22.15 million passengers used this network and 3.32 million metric tons of goods were also shipped daily from 2019 to 2020. The national rail network comprised 126,366 km of track over a route of 67,368 km and 7,325 stations. It is the fourth-largest national railway network globally after the United States, Russia and China. But with the passage, they pose a threat to the general public while travelling, being the instances of crimes rising fourfold in rails. The ongoing railway crime has become a cause of concern for the common passenger now. In this article, F-index for fuzzy graphs is used to analyze the railway crimes in India and compared with three other topological indices. F-index for fuzzy graphs and the first Zagreb index for fuzzy graphs provide similar results whereas F-index for fuzzy graphs provides better realistic results than F-index for crisp graphs and first Zagreb index for crisp graphs to detect the crime in Indian railway. Also, this index is studied for several operations such as Cartesian product, composition, union and join of two fuzzy graphs. Some interesting relations of F-index are established during fuzzy graph transformations. Using those transformation, it is shown that n-vertex star has maximum F-index among the n-vertex trees. Also, maximal n-vertex unicyclic fuzzy graph having r cycle is determined with respect to F-index. Springer Berlin Heidelberg 2022-05-18 2023 /pmc/articles/PMC9116720/ /pubmed/35607521 http://dx.doi.org/10.1007/s12190-022-01748-5 Text en © The Author(s) under exclusive licence to Korean Society for Informatics and Computational Applied Mathematics 2022 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic. |
spellingShingle | Original Research Islam, Sk Rabiul Pal, Madhumangal Further development of F-index for fuzzy graph and its application in Indian railway crime |
title | Further development of F-index for fuzzy graph and its application in Indian railway crime |
title_full | Further development of F-index for fuzzy graph and its application in Indian railway crime |
title_fullStr | Further development of F-index for fuzzy graph and its application in Indian railway crime |
title_full_unstemmed | Further development of F-index for fuzzy graph and its application in Indian railway crime |
title_short | Further development of F-index for fuzzy graph and its application in Indian railway crime |
title_sort | further development of f-index for fuzzy graph and its application in indian railway crime |
topic | Original Research |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9116720/ https://www.ncbi.nlm.nih.gov/pubmed/35607521 http://dx.doi.org/10.1007/s12190-022-01748-5 |
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