TY - JOUR

T1 - Neighborhood Versions of Geometric–Arithmetic and Atom Bond Connectivity Indices of Some Popular Graphs and Their Properties

AU - Abubakar, Muhammad Shafii

AU - Aremu, Kazeem Olalekan

AU - Aphane, Maggie

N1 - Funding Information:
The APC was funded by the Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences, Pretoria, South Africa.
Publisher Copyright:
© 2022 by the authors.

PY - 2022/9

Y1 - 2022/9

N2 - 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.

AB - 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.

KW - atom bond connectivity index

KW - degree-based topological indices

KW - geometric–arithmetic index

KW - neigborhood degree sum

KW - neigborhood topological indices

UR - http://www.scopus.com/inward/record.url?scp=85138736063&partnerID=8YFLogxK

U2 - 10.3390/axioms11090487

DO - 10.3390/axioms11090487

M3 - Article

AN - SCOPUS:85138736063

VL - 11

JO - Axioms

JF - Axioms

SN - 2075-1680

IS - 9

M1 - 487

ER -