id: 06026732
dt: j
an: 06026732
au: Mane, S.A.; Waphare, B.N.
ti: Regular connected bipancyclic spanning subgraphs of hypercubes.
so: Comput. Math. Appl. 62, No. 9, 3551-3554 (2011).
py: 2011
pu: Elsevier Science Ltd. (Pergamon), Oxford
la: EN
cc: 
ut: regular; connected; spanning; bipancyclic; subgraphs; hypercubes
ci: 
li: doi:10.1016/j.camwa.2011.08.071
ab: Summary: An $n$-dimensional hypercube $Q_{n}$ is a Hamiltonian graph; in
    other words $Q_{n}$ ($n\ge 2$) contains a spanning subgraph which is
    $2$-regular and $2$-connected. In this paper, we explore yet another
    strong property of hypercubes. We prove that for any integer $k$ with
    $3\le k\le n$, $Q_{n}$ ($n\ge 3$) contains a spanning subgraph which is
    $k$-regular, $k$-connected and bipancyclic. We also obtain the result
    that every mesh $P_{m}\times P_{n}$ ($m,n\ge 2$) is bipancyclic, which
    is used to prove the property above.
rv: