On Large Sets of \(K_{1,p}\)-Decomposition of Complete Bipartite Graphs

Let \( H \) and \( G \) be two simple graphs, where \( G \) is a subgraph of \( H \). A \( G \)-decomposition of \( \lambda H \), denoted by \( (\lambda H, G) \)-GD, is a partition of all the edges of \( \lambda H \) into subgraphs (G-blocks), each of which is isomorphic to \( G \). A large set of \( (\lambda H, G) \)-GD, denoted by \( (\lambda H, G) \)-LGD, is a partition of all subgraphs isomorphic to \( G \) of \( H \) into \( (\lambda H, G) \)-GDs (called small sets). In this paper, we investigate the existence of \( (\lambda K_{mn}, K_{1,p}) \)-LGD and obtain some existence results, where \( p \geq 3 \) is a prime.