부산대학교 도서관

AbstractThe n-dimensional augmented cube AQnis a variation of the hypercube It is a -regular and -connected graph on vertices. One of the fundamental properties of AQnis 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 AQnwith contains a 4-regular, 4-connected and pancyclic subgraph on lvertices if and only if Also, we establish that for every even integer lfrom 4 to there exists a 3-regular, 3-connected and pancyclic subgraph of AQnon lvertices.