Decomposition of hypercubes into sunlet graphs

A. V. Sonawane

paper

Decomposition of hypercubes into sunlet graphs

arXiv:2107.10313

Abstract

For any positive integer $k \geq 3,$ the sunlet graph of order $2 k$ , denoted by $L_{2 k},$ is the graph obtained by adding a pendant edge to each vertex of a cycle of length $k .$ In this paper, we prove that the necessary and sufficient condition for the existence of an $L_{16}$ -decomposition of the $n$ -dimensional hypercube $Q_{n}$ is $n = 4$ or $n \geq 6.$ Also, we prove that for any integer $m \geq 2,$ $Q_{mn}$ has an $L_{2 k}$ -decomposition if $Q_{n}$ has a $C_{k}$ -decomposition.

10 pages, 4 figures