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 Title: The super spanning connectivity and super spanning laceability of the enhanced hypercubes Authors: Chang,CH;Lin,CK;Tan,JJM;Huang,HM;Hsu,LH Contributors: 數學研究所 Keywords: GRAPHS;NETWORKS Date: 2009 Issue Date: 2010-06-29 19:39:06 (UTC+8) Publisher: 中央大學 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 1a parts per thousand currency signka parts per thousand currency sign kappa(G) where kappa(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 1a parts per thousand currency signka parts per thousand currency sign kappa(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. Relation: JOURNAL OF SUPERCOMPUTING Appears in Collections: [數學研究所] 期刊論文

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