Iranian Journal of Mathematical Chemistry

Iranian Journal of Mathematical Chemistry

A Note on the General Gutman Index of Graphs

Document Type : Research Paper

Authors
Zohreh Jamalkashani 1
‎Gholam Hossein Fath-Tabar 1
Mahdi Sabzevari 2
1 Department of Pure Mathematics‎, ‎Faculty of Mathematical Sciences‎, ‎University of Kashan‎, ‎Kashan‎, ‎Iran
2 Department of Applied Mathematics‎, ‎Faculty of Mathematical Sciences‎, ‎University of Kashan‎, ‎Kashan‎, ‎Iran
10.22052/ijmc.2025.257853.2079
Abstract
‎The general Gutman index‎, ‎denoted by $G_{a,b}(H)$‎, ‎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 $G_{2,1}(H)$‎. ‎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.
Keywords
General Gutman index
Pendant vertex
Bicyclic graphs
Subjects
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Iranian Journal of Mathematical Chemistry
Volume 17, Issue 3
In Progress
Summer 2026
Pages 271-285