First Zagreb index of fuzzy transformation graphs

Article type: Research Article

Authors: Leena Rosalind Mary, G. | Deepa, G.^{; *}

Affiliations: Department of Mathematics, Vellore Institute of Technology, Vellore, Tamil Nadu, India

Correspondence: [*] Corresponding author. G. Deepa. Department of Mathematics, Vellore Institute of Technology, Vellore, Tamil Nadu, India. E-mail: deepa.g@vit.ac.in.

Abstract: The first Zagreb index is equal to the sum of the squares of the degrees at each vertex of G. In this study, we create four distinct types of fuzzy transformation graphs and investigate the fundamental characteristics shared by them. Additionally, upper bounds on the first Zagreb index of fuzzy transformation graphs in terms of fuzzy graph G elements have been discovered.

Keywords: Fuzzy graph, fuzzy transformation graph, first Zagreb index

DOI: 10.3233/JIFS-221781

Journal: Journal of Intelligent & Fuzzy Systems, vol. 44, no. 5, pp. 7169-7180, 2023