The Hyper-Zagreb Index of Trees and Unicyclic Graphs
Hassan Rezapour, Ramin Nasiri, Seyedahmad Mousavi
TL;DR
This paper characterizes trees and unicyclic graphs with the highest Hyper-Zagreb index values, which combines first and second Zagreb indices, motivated by applications in chemistry.
Contribution
It provides a complete characterization of extremal trees and unicyclic graphs based on the Hyper-Zagreb index, a novel topological measure.
Findings
Identifies trees with the top four greatest HM-values.
Identifies unicyclic graphs with the top eight greatest HM-values.
Highlights the importance of HM in chemical graph theory.
Abstract
Applications in chemistry motivated mathematicians to define different topological indices for different types of graphs. The Hyper-Zagreb index (HM) is an important tool as it integrates the first and the second Zagreb indices. In this paper, we characterize the trees and unicyclic graphs with the first four and first eight greatest HM-value, respectively.
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Taxonomy
TopicsGraph theory and applications · Computational Drug Discovery Methods · History and advancements in chemistry