ON ARITHMETIC-GEOMETRIC INDEX (GA) AND EDGE GA INDEX

V.AYTAC, T.TURACI

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Abstract

Let G(V (G);E(G)) be a simple connected graph and dG(u) be the degree of the vertex u. Topological indices are numerical parameters of a graph which are invariant under graph isomorphisms. Recently, people are studying various topological measures such as the arithmetic-geometric index and the edge version of arithmetic- geometric index of a graph G. Topological index based on the ratios of geometrical and arithmetical means of end vertex degrees of edges. In this paper, exact values for the arithmetic-geometric index and the edge version of arithmetic-geometric index of wheel related graphs namely gear, helm, sun ower and friendship graph are obtained.

Keywords

Arithmetic-Geometric Index; Edge Arithmetic-Geometric Index; Network Design and Communication; Gear graph; Helm graph; Sun ower graph; Friendship graph