Maximum Modified Sombor Index of Unicyclic Graphs with Given Girth

Document Type : Research Paper

Authors

1 Department of Mathematics‎, ‎Kongu Arts and Science College (Autonomous)‎, ‎Erode‎, ‎Tamilnadu-638 107

2 Department of Mathematics‎, ‎AVP College of Arts and Science‎, ‎Tirupur-641 652

Abstract

‎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.

Keywords

References

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Iranian Journal of Mathematical Chemistry
Volume 15, Issue 2
June 2024
Pages 117-122

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