Sunlet Decomposition of Certain Equipartite Graphs

Abstract

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.

Prime Decomposition of Zero Divisor Graph in a Commutative Ring

“…e concept of a zero divisor graph is a commutative ring was proposed by Beck's [2]. e general terminology and notation everything based on the papers [ [3][4][5][6][7]]. In this paper, we investigate the prime decomposition of Γ(Z pq ) into K 1,m i star graph with m i edges and obtain the following results.…”