ScholarWorks@성균관대학교

초록

The Augmented Sombor index of a connected graph G with at least three vertices is defined as(formula presented) where di and dj denote the degrees of the vertices vi and vj, re¬spectively. In this paper, we examine the chemical applicability of the ASO index for predicting thirteen physicochemical properties of octane isomers. We also characterize extremal graphs with re¬spect to the ASO index over the following three classes of graphs with a given order: (i) trees, (ii) quasi-trees (where a quasi-tree is a connected graph that becomes a tree upon the removal of a single vertex), and (iii) connected graphs. Furthermore, we determine the unique graph minimizing the ASO index among all unicyclic graphs of fixed order. Finally, we conclude the paper by outlining potential directions for future research related to the AS O index.