Decomposition of Augmented Cubes into Regular Connected Pancyclic Subgraphs

S. A. Kandekar; Y. M. Borse; B. N. Waphare

Decomposition of Augmented Cubes into Regular Connected Pancyclic Subgraphs

Combinatorics 2018-09-12 v1

Authors: S. A. Kandekar , Y. M. Borse , B. N. Waphare

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 $n_i \geq 3.$

Cite

@article{arxiv.1809.03493,
  title  = {Decomposition of Augmented Cubes into Regular Connected Pancyclic Subgraphs},
  author = {S. A. Kandekar and Y. M. Borse and B. N. Waphare},
  journal= {arXiv preprint arXiv:1809.03493},
  year   = {2018}
}

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