K-n (lambda) IS FULLY {P-7, S-4}-DECOMPOSABLE

Let Pk+1 denote a path of length k, S-m denote a star with m edges, and K-n (lambda) denote the complete multigraph on n vertices in which every pair of distinct vertices is joined by lambda edges. In this paper, we have obtained the necessary conditions for a {Pk+1, S-m}-decomposition of K-n (lambda) and proved that the necessary conditions are also sufficient when k = 6 and m = 4.