Sunlet decomposition of certain equipartite graphs (Q1953667)

Summary: Let \(L_{2n}\) stand for the sunlet graph which is a graph that consists of a cycle and an edge terminating in a vertex of degree one attached to each vertex of cycle \(C_n\). The necessary condition for the equipartite graph \(K_n + I \ast \bar{K}_m\) to be decomposed into \(L_{2n}\) for \(n \geq 2\) is that the order of \(L_{2n}\) must divide \(n^2m^2/2\), the order of \(K_n + I \ast \bar{K}_m\). In this work, we show that this condition is sufficient for the decomposition. The proofs are constructive using graph theory techniques.