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arXiv · 1809.03493

Decomposition of Augmented Cubes into Regular Connected Pancyclic Subgraphs

S. A. Kandekar·Y. M. Borse·B. N. Waphare
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Abstract

In this paper, we consider the problem of decomposing the augmented cube $AQ_n$ into two spanning, regular, connected and pancyclic subgraphs. We prove that for $ n \geq 4$ and $ 2n - 1 = n_1 + n_2 $ with $ n_1, n_2 \geq 2,$ the augmented cube $ AQ_n$ can be decomposed into two spanning subgraphs $ H_1$ and $ H_2$ such that each $ H_i$ is $n_i$-regular and $n_i$-connected. Moreover, $H_i$ is $4$-pancyclic if $ n_i \geq 3.$

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S. A. Kandekar, Y. M. Borse, B. N. Waphare. 2018-09-10. Decomposition of Augmented Cubes into Regular Connected Pancyclic Subgraphs. https://arxiv.org/abs/1809.03493

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