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Even Star Decomposition of Complete Bipartite Graphs

A decomposition (G1, G2, G3,… , Gn) of a graph G is an Arithmetic Decomposition(AD) if |E(Gi)| = 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,… , G2n).

Canadian Center of Science and Education

E. Ebin Raja Merly J. Suthiesh Goldy

Journal of Mathematics Research

2016

Title: Even Star Decomposition of Complete Bipartite Graphs

Description:

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,… , G2n).

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