Decomposition of cartesian product of complete graphs into sunlet graphs of order eight

Abstract

For any integer $k\geq 3$, we define the sunlet graph of order 2k, denoted by $L_{2k}$, as the graph consisting of a cycle of length k together with k pendant vertices such that, each pendant vertex adjacent to exactly one vertex of the cycle so that the degree of each vertex in the cycle is 3. In this paper, we establish necessary and sufficient conditions for the existence of decomposition of the Cartesian product of complete graphs into sunlet graphs of order eight.

Received: 24 January 2021 | Accepted: 25 November 2021