Decomposition of hypercubes into sunlet graphs

A. V. Sonawane

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arXiv · 2107.10313

Decomposition of hypercubes into sunlet graphs

A. V. Sonawane

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Abstract

For any positive integer $k \geq 3,$ the sunlet graph of order $2k$, denoted by $L_{2k},$ 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 $L_{2k}$-decomposition if $Q_{n}$ has a $C_k$-decomposition.

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A. V. Sonawane. 2021-07-21. Decomposition of hypercubes into sunlet graphs. https://arxiv.org/abs/2107.10313

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