Decomposition of the complete bipartite graphs plus a 1-factor Km,m⊕I into paths and cycles of length four.

Let Km,m be the complete bipartite graph with m vertices in each partite set and Km,m⊕I indicates Km,m with a 1-factor added. In this Paper, We investigated the necessary and sufficient conditions for the existence of {λP5, µC4}−decomposition of Km,m ⊕ I when m ≡ 3 (mod 4) and λ ≠ 1. [ABSTRACT FROM AUTHOR]