Arithmetico geometric decomposition of some graphs

Abstract

A decomposition (G_ab, G_(a+d)br, …, G_(a+(n-1)d)br^n-1) of G is said to be a Arithmetico Geometric Decomposition (ACOGD) or (a, d, b, r, n) – Decomposable if each G_(a+(i-1)d)br^i-1 is connected and |E(G_(a+(i-1)d)br^i-1)| = (a + (i - 1)d) _br^i-1 for every i = 1, 2, ...., n and a, d, b, r (>1) ∈ N. Clearly, q = b(a-(a+(n-1)d) r^n)/(1-r) + dbr(1-r^(n-1)/(1-r)^2, for every n∈ N. In this paper, we seek to find Arithmetico Geometric Decomposition of some graphs.