Upper and lower bounds for topological indices on unicyclic graphs
\'Alvaro Mart\'inez-P\'erez, Jos\'e M. Rodr\'iguez
TL;DR
This paper establishes new bounds for various topological indices on unicyclic graphs, characterizing extremal graphs and considering parameters like maximum degree and pendant vertices.
Contribution
It introduces novel inequalities for multiple topological indices on unicyclic graphs and characterizes extremal graphs for these indices.
Findings
Derived upper and lower bounds for topological indices.
Characterized extremal unicyclic graphs for these bounds.
Analyzed effects of maximum degree and pendant vertices.
Abstract
The aim of this paper is to obtain new inequalities for a large family of topological indices restricted to unicyclic graphs and to characterize the set of extremal unicyclic graphs with respect to them. This family includes variable first Zagreb, variable sum exdeg, multiplicative second Zagreb and Narumi-Katayama indices. Our main results provide upper and lower bounds for these topological indices on unicyclic graphs, fixing or not the maximum degree or the number of pendant vertices.
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Taxonomy
TopicsGraph theory and applications · Synthesis and Properties of Aromatic Compounds · Metal-Organic Frameworks: Synthesis and Applications