A Note on the General Gutman Index of Graphs

Abstract

The general Gutman index, denoted by Ga;b(H), is a prominent distance–degree-based topological index in chemical graph theory, defined using a combination of vertex degrees and intervertex distances. In this paper, we focus on bicyclic graphs as a special class of graphs and investigate the behavior of this index within that setting. In particular, we examine the case G2;1(H). The primary objective of this study is to establish a sharp upper bound for the general Gutman index in bicyclic graphs. By exploiting the structural properties of bicyclic graphs and employing combinatorial techniques, we derive a sharp upper bound for this index. The results obtained may provide a useful foundation for further research on distance-degree-based indices and their structural implications in mathematical chemistry.