Even Star Decomposition of Complete Bipartite Graphs


  •  E. Ebin Merly    
  •  J. Goldy    

Abstract

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, dZ+. 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).

 



This work is licensed under a Creative Commons Attribution 4.0 License.
  • ISSN(Print): 1916-9795
  • ISSN(Online): 1916-9809
  • Started: 2009
  • Frequency: bimonthly

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