An Isomorphic Decomposition of \(K_{24}\)

A decomposition of a graph \(H\) is a family of subgraphs of \(H\) such that each edge of \(H\) is contained in exactly one member of the family. For a graph \(G\), a \(G\)-decomposition of the graph \(H\) is a decomposition of \(H\) into subgraphs isomorphic to \(G\). If \(H\) has a \(G\)-decomposition, \(H\) is said to be \(G\)-decomposable; this is denoted by \(H \rightarrow G\). In this paper, we prove by construction that the complete graph \(K_{24}\) is \(G\)-decomposable, where \(G\) is the complementary graph of the path \(P_5\).