ARITHMETIC ODD DECOMPOSITION OF GRAPHS

The most important area in graph theory is graph decomposition [10]. Graph decomposition was first introduced by the mathematician Konig in 1960.Graph decomposition usually means collection of edge disjoint subgraphs such that each edge is appropriate to accurately unique. If every contains a trail or a cycle formerly we usually named it as path decomposition or cycle decomposition [1,6,9]. N. Gnana Dhas and J. Paul Raj Joseph [7] modified Ascending Subgraph Decomposition and introduced the concept known as Continous Monotonic Decomposition of graphs for connected graphs. An essential and adequate form aimed at a connected simple graph to admit Continous Monotonic Decomposition was framed and a host of graphs declare Continous Monotonic Decomposition were itemized[2].A decomposition (G₁, G₂,…,G_n ) of G is supposed to be  Arithmetic Decomposition if  for every  i = 1,2,3,…,n and a,d ϵG. Clearly . If a = 1 and d = 1 then . Ebin Raja Merly and N. Gnanadhas [4,5] defined the concept of Arithmetic Odd Decomposition of graphs. A Decomposition (G₁, G₃, G_5,…,G_2n-1) is said to be arithmetic odd decomposition when a =1 and d = 2. Further AOD for some special class of graphs, namely W_n, 𝐾_1,n ˄𝐾₂ and 𝐶_n ˄𝑃₃ are studied[11,13]. This paper deals with theArithmetic odd decomposition of some graphs like tensor product of Cycle with  Bistar graph B_n,_n and  tensor product of a Path P_n with K_2.