On the Augmented Sombor Index of Graphs
Abstract
Let G be a connected graph having more than two vertices andIt is known that the cycle graph Cn uniquely minimizes the ASO index in the class of all n-order unicyclic graphs.In this paper, we prove that the unique n-order unicyclic graph of maximum degree n -1 maximizes the ASO index in the aforementioned unicyclic graph class.We also prove that ASO(G -vivj) < ASO(G) whenever neither of the graphs G -vivj and G contains any isolated edge.Utilizing this edge-deletion property, we characterize the unique graph maximizing the ASO index among all fixed-order connected graphs with a specified vertex connectivity (or edge connectivity).
Fields of Study & Subjects
Graph theory and applications
Graph Labeling and Dimension Problems
Advanced Graph Theory Research
Publication details
- Journal / source
- match Communications in Mathematical and in Computer Chemistry
- Publisher
- University Library in Kragujevac
- Volume
- 2
- Issue
- 96
- Pages
- 587–587
- Publication date
- 30 January 2026