On regular subgraphs of augmented cubes

Abstract

The n-dimensional augmented cube AQn is a variation of the hypercube It is a -regular and -connected graph on vertices. One of the fundamental properties of AQn is that it is pancyclic, that is, it contains a cycle of every length from 3 to In this paper, we generalize this property to k-regular subgraphs for and We prove that the augmented cube AQn with contains a 4-regular, 4-connected and pancyclic subgraph on l vertices if and only if Also, we establish that for every even integer l from 4 to there exists a 3-regular, 3-connected and pancyclic subgraph of AQn on l vertices.

Keywords

• augmented cube
• hypercube
• regular subgraph
• pancyclicity
• connectivity