Abstract
Connectivity measures real energization state of manifold applications and user interference in many criteria-based network systems. Randic index is a parameter of this type that can be used to measure the combined power of molecular graph or graphical network system. The concept of Randic index has been applied in a connected system in Indonesia tourism sectors under some uncertain conditions. First, Randic index of fuzzy graph (FG) and fuzzy subgraph are introduced and investigated their properties. Second, different upper and lower bounds of Randic index and their isomorphic properties in fuzzy graphs are exhibited. Third, the Randic index in directed fuzzy graph (FDG) is introduced. Due to presence of similar contribution of vertices, many formulas for calculating Randic index of regular fuzzy graphs are presented. Fourth, some similarity and distinction of Randic index with connectivity index (CI) and Wiener index (WI) in fuzzy graph are analyzed. Fifth, an algorithm and a flowchart are proposed to determine Randic index in a fuzzy graph. Finally, an application is depicted to mention the order of important crossroads and stoppages between Balai Kemambang (BKB) and Bukit Kendalisada (BKS) in Indonesia tourism sectors.
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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.
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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 second author acknowledges the support given by the DST-FIST, INDIA (Sanction Order No.: SR/FST/MS-1/2018/21(C) dated-13/12/2019) for up-gradation of research facility at the departmental level.
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SP: conceptualization, methodology, formal analysis, and writing—original draft preparation. GG: conceptualization, methodology, investigation, formal analysis, supervision, writing—review and editing, visualization, and validation. QX: investigation, formal analysis, visualization, and validation
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Poulik, S., Ghorai, G. & Xin, Q. Explication of crossroads order based on Randic index of graph with fuzzy information. Soft Comput 28, 1851–1864 (2024). https://doi.org/10.1007/s00500-023-09453-6
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DOI: https://doi.org/10.1007/s00500-023-09453-6