ScholarWorks@성균관대학교

초록

Let G be a connected graph having more than two vertices and let di denote the degree of vertex vi in G. Let E(G) represent the edge set of G. Then, the augmented Sombor (ASO) index of G is defined as (Formula presented). It 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).