### Abstract

A k-container C(u, v) of G between u and v is a set of k internally disjoint paths between u and v. A k-container C(u, v) of G is a k*-container if it contains all nodes of G. A graph G is k*-connected if there exists a k*-container between any two distinct nodes. The spanning connectivity of G, kappa* (G), is defined to be the largest integer k such that G is omega*-connected for all 1 <= omega <= k if G is an 1*-connected graph and undefined if otherwise. A graph G is super spanning connected if kappa*(G) = kappa(G). In this paper, we prove that the n-dimensional augmented cube AQ(n) is super spanning connected.

Original language | English |
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Pages (from-to) | 161-177 |

Journal | Ars Combinatoria |

Volume | 104 |

State | Published - Apr 2012 |

### Keywords

- hamiltonian; hamiltonian connected; container; connectivity

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## Cite this

Lin, C-K., Ho, T-Y., Tan, J-M., & Hsu, L. H. (2012). Super Spanning Connectivity of Augmented Cubes.

*Ars Combinatoria*,*104*, 161-177.