Abstract: | Let G = (V(G),E(G)) be a graph. A (ν, G, λ)‐GD is a partition of all the edges of λKν into subgraphs (G‐blocks), each of which is isomorphic to G. The (ν, G, λ)‐GD is named as graph design for G or G‐decomposition. The large set of (ν, G, λ)‐GD is denoted by (ν, G, λ)‐LGD. In this paper, we obtain a general result by using the finite fields, that is, if q ≥ k ≥ 2 is an odd prime power, then there exists a (q,Pk, k ? 1)‐LGD. © 2005 Wiley Periodicals, Inc. J Combin Designs. |