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,…,Gn ) 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, G5,…,G2n-1) is said to be arithmetic odd decomposition when a =1 and d = 2. Further AOD for some special class of graphs, namely Wn, 𝐾1,n ˄𝐾2 and 𝐶n ˄𝑃3 are studied[11,13]. This paper deals with theArithmetic odd decomposition of some graphs like tensor product of Cycle with Bistar graph Bn,n and tensor product of a Path Pn with K2.

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