Decompositions of Various Complete Graphs into Isomorphic Copies of 4-cycles with Three Pendant Edges

An \( H \)-decomposition of a graph \( G \) is a partition of the edges of \( G \) into copies isomorphic to \( H \). When the decomposition is not feasible, one looks for the best possible by minimizing: the number of unused edges (leave of a packing), or the number of reused edges (padding of a covering). We consider the \( H \)-decomposition, packing, and covering of the complete graphs and complete bipartite graphs, where \( H \) is a 4-cycle with three pendant edges.