Neighborhood Versions of Geometric–Arithmetic and Atom Bond Connectivity Indices of Some Popular Graphs and Their Properties

Muhammad Shafii Abubakar, Kazeem Olalekan Aremu*, Maggie Aphane

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this article, we introduce the neighborhood versions of two classical topological indices, namely neighborhood geometric–arithmetic and neighborhood atom bond connectivity indices. We study the graph-theoretic properties of these new topological indices for some known graphs, e.g., complete graph (Formula presented.), regular graph (Formula presented.), cycle graph (Formula presented.), star graph (Formula presented.), pendant graph, and irregular graph and further establish their respective bounds. We note that the neighbourhood geometric–arithmetic index of (Formula presented.), (Formula presented.), (Formula presented.), and (Formula presented.) is equal to the number of edges. The neighborhood atom bond connectivity index of an arbitrary simple graph (Formula presented.) is strictly less than the number of edges. Our results contribute to the literature in this direction.

Original languageEnglish
Article number487
JournalAxioms
Volume11
Issue number9
DOIs
Publication statusPublished - Sep 2022

Keywords

  • atom bond connectivity index
  • degree-based topological indices
  • geometric–arithmetic index
  • neigborhood degree sum
  • neigborhood topological indices

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