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The super spanning connectivity and super spanning laceability of the enhanced hypercubes

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Abstract

A k -container C(u,v) of a graph G is a set of k disjoint paths between u and v. A k-container C(u,v) of G is a k * -container if it contains all vertices of G. A graph G is k * -connected if there exists a k *-container between any two distinct vertices of G. Therefore, a graph is 1*-connected (respectively, 2*-connected) if and only if it is Hamiltonian connected (respectively, Hamiltonian). A graph G is super spanning connected if there exists a k *-container between any two distinct vertices of G for every k with 1≤kκ(G) where κ(G) is the connectivity of G. A bipartite graph G is k * -laceable if there exists a k *-container between any two vertices from different partite set of G. A bipartite graph G is super spanning laceable if there exists a k *-container between any two vertices from different partite set of G for every k with 1≤kκ(G). In this paper, we prove that the enhanced hypercube Q n,m is super spanning laceable if m is an odd integer and super spanning connected if otherwise.

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Correspondence to Chung-Hao Chang.

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Chang, CH., Lin, CK., Tan, J.J.M. et al. The super spanning connectivity and super spanning laceability of the enhanced hypercubes. J Supercomput 48, 66–87 (2009). https://doi.org/10.1007/s11227-008-0206-0

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  • DOI: https://doi.org/10.1007/s11227-008-0206-0

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