Decomposition of Product Graphs into Paths and Cycles of Length Four

Abstract

Let $$P_{k}$$Pk and $$C_k$$Ck respectively denote a path and a cycle on $$k$$k vertices. In this paper we give necessary and sufficient conditions for the existence of $$\{P_{5}, C_4\}_{\{p, q\}}$${P5,C4}{p,q}-decomposition of tensor product and cartesian product of complete graphs. Further we extent such decomposition to complete multipartite graphs.