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

Year 2022, Volume: 9 Issue: 1, 29 - 46, 15.01.2022

Kaliappan Sowndhariya Appu Muthusamy

https://doi.org/10.13069/jacodesmath.1056547

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.

Keywords

Graph decomposition , Cartesian product , Corona graph , Sunlet graph

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