Decomposition of Augmented Cubes into Regular Connected Pancyclic Subgraphs

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

paper

Decomposition of Augmented Cubes into Regular Connected Pancyclic Subgraphs

arXiv:1809.03493

Abstract

In this paper, we consider the problem of decomposing the augmented cube $A Q_{n}$ into two spanning, regular, connected and pancyclic subgraphs. We prove that for $n \geq 4$ and $2 n - 1 = n_{1} + n_{2}$ with $n_{1}, n_{2} \geq 2,$ the augmented cube $A Q_{n}$ 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 $n_{i} \geq 3.$