Sunlet Decomposition of Certain Equipartite Graphs

Abstract EN

Let L2n 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 Cn.

The necessary condition for the equipartite graph Kn+I*K̅m to be decomposed into L2n for n≥2 is that the order of L2n must divide n2m2/2, the order of Kn+I*K̅m.

In this work, we show that this condition is sufficient for the decomposition.

The proofs are constructive using graph theory techniques.