On the third ABC index of trees and unicyclic graphs
Rui Song

TL;DR
This paper investigates the maximum third atom-bond connectivity index ($ABC_3$) for unicyclic graphs with fixed girth and trees with fixed diameter, providing exact characterizations of the extremal graphs.
Contribution
It determines the maximal $ABC_3$ index for specific classes of graphs and characterizes the extremal structures, advancing understanding of this index in graph theory.
Findings
Identified the maximum $ABC_3$ index for unicyclic graphs with given girth.
Determined the maximum $ABC_3$ index for trees with given diameter.
Characterized the extremal graphs achieving these maxima.
Abstract
Let be a simple connected graph with vertex set and edge set . The third atom-bond connectivity index, index, of is defined as , where eccentricity is the largest distance between and any other vertex of , namely . This work determines the maximal index of unicyclic graphs with any given girth and trees with any given diameter, and characterizes the corresponding graphs.
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Taxonomy
TopicsGraph theory and applications · Supramolecular Self-Assembly in Materials · Synthesis and Properties of Aromatic Compounds
