On Arithmetic-Geometric Index (Ga) and Edge Ga Index

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 arithmeticgeometric 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, sunflower and friendship graph are obtained.

The majestic edge coloring and the majestic 2-tone edge coloring of some cycle related graphs

“…The cycle related graphs are wheel, helm, gear, friendship, and web graph. These graphs are especially used in the network [2], [6], [10]. Graph coloring is important to strengthen a network or to find faulty computers.…”