3-extraconnectivity of Cayley Graphs Generated by Transposition Generating Trees

给定一个图g和一个非负整数g,若图g中存在(边)点集,使得删除该集合后图g不连通并且每个连通分支的点数大于g,所有这样的(边)点集的最小基数,称为g-额外(边)连通度(记作κg(g)(λg(g)).本文将确定由对换树生成的凯莱图的3-额外(边)连通度(记作κ3(λ3).Given a graph G and a non-negative integer g, the g-extra(edge) connectivity of G (written κg(G)(λg(G))is the minimum cardinality of a set of (edges)vertices of G, if any, whose deletion disconnects G, and every remaining component has more than g vertices.In this paper, we determine 3-extra(edge) connectivity(written κ3(λ3)) of Cayley graphs generated by transposition trees.supportedbyNSFC(No.10671165

Disjoint Hamilton cycles in transposition graphs

Most network topologies that have been studied have been subgraphs of transposition graphs. Edge-disjoint Hamilton cycles are important in network topologies for improving fault-tolerance and distribution of messaging traffic over the network. Not much was known about edge-disjoint Hamilton cycles in general transposition graphs until recently Hung produced a construction of 4 edge-disjoint Hamilton cycles in the 5-dimensional transposition graph and showed how edge-disjoint Hamilton cycles in (n + 1)-dimensional transposition graphs can be constructed inductively from edge-disjoint Hamilton cycles in n-dimensional transposition graphs. In the same work it was conjectured that n-dimensional transposition graphs have n − 1 edge-disjoint Hamilton cycles for all n greater than or equal to 5. In this paper we provide an edge-labelling for transposition graphs and, by considering known Hamilton cycles in labelled star subgraphs of transposition graphs, are able to provide an extra edge-disjoint Hamilton cycle at the inductive step from dimension n to n + 1, and thereby prove the conjecture

Disjoint Hamilton cycles in transposition graphs

This paper was accepted for publication in the journal Discrete Applied Mathematics and the definitive published version is available at http://dx.doi.org/10.1016/j.dam.2016.02.007.Most network topologies that have been studied have been subgraphs of transposition graphs. Edge-disjoint Hamilton cycles are important in network topologies for improving fault-tolerance and distribution of messaging traffic over the network. Not much was known about edge-disjoint Hamilton cycles in general transposition graphs until recently Hung produced a construction of 4 edge-disjoint Hamilton cycles in the 5-dimensional transposition graph and showed how edge-disjoint Hamilton cycles in (n + 1)-dimensional transposition graphs can be constructed inductively from edge-disjoint Hamilton cycles in n-dimensional transposition graphs. In the same work it was conjectured that n-dimensional transposition graphs have n − 1 edge-disjoint Hamilton cycles for all n greater than or equal to 5. In this paper we provide an edge-labelling for transposition graphs and, by considering known Hamilton cycles in labelled star subgraphs of transposition graphs, are able to provide an extra edge-disjoint Hamilton cycle at the inductive step from dimension n to n + 1, and thereby prove the conjecture