Abstract

A decomposition (G₁, G₂, G₃,… , G_n) of a graph G is an Arithmetic Decomposition(AD) if |E(G_i)| = a + (i – 1)d for all i = 1, 2,… , n and a, d∈Z⁺. Clearly q = n/2 [2a + (n – 1)d]. The AD is a CMD if a = 1 and d = 1. In this paper we introduced the new concept Even Decomposition of graphs. If a = 2 and d = 2 in AD, then q = n(n + 1). That is, the number of edges of G is the sum of first n even numbers 2, 4, 6,… , 2n. Thus we call the AD with a = 2 and d = 2 as Even Decomposition. Since the number of edges of each subgraph of G is even, we denote the Even Decomposition as (G₂, G₄,… , G_2n).

 

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