University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 15 2 2024 06 01 Maximum Modified Sombor Index of Unicyclic Graphs with Given Girth 117 122 114372 10.22052/ijmc.2023.253810.1780 EN Sethumadhavan Nagarajan Department of Mathematics‎, ‎Kongu Arts and Science College (Autonomous)‎, ‎Erode‎, ‎Tamilnadu-638 107 A‎. ‎Vijaya Department of Mathematics‎, ‎AVP College of Arts and Science‎, ‎Tirupur-641 652 Journal Article 2023 11 18 ‎For any graph $G$‎, ‎the modified Sombor index is defined as the reciprocal of the well-known Sombor Index‎. ‎The girth of $G$‎, ‎by short $g(G)$‎, ‎is the length of the smallest cycle in $G$‎. ‎A graph with exactly one cycle is a unicyclic graph‎. ‎If it is further‎, ‎connected‎, ‎it is a connected unicyclic graph‎. ‎In this article‎, ‎we achieved the modified Sombor index for a collection of graphs‎, ‎connected unicyclic graphs and also obtained the maximum modified Sombor index for the class of unicyclic graphs based on the restrictions by a fixed girth‎. https://ijmc.kashanu.ac.ir/article_114372_b2f3d5efe1ca8e26c74d8f640f787deb.pdf