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Short containers in Cayley graphs

机译:Cayley图中的短容器

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The star diameter of a graph measures the minimum distance from any source node to several other target nodes in the graph. For a class of Cayley graphs from abelian groups, a good upper bound for their star diameters is given in terms of the usual diameters and the orders of elements in the generating subsets. This bound is tight for several classes of graphs including hypercubes and directed n-dimensional tori. The technique used is the so-called disjoint ordering for a system of subsets, due to Gao, Novick and Qju [S. Gao, B. Novick, K. Qiu, From Hall's matching theorem to optimal routing on hypercubes, J. Comb. Theory B 74 (1998) 291-301].
机译:图的星形直径测量从图中任何源节点到其他几个目标节点的最小距离。对于来自阿贝尔群的一类Cayley图,根据通常的直径和生成子集中元素的顺序,给出了其星形直径的良好上限。对于几类图(包括超立方体和有向n维花托),该边界是严格的。由于Gao,Novick和Qju所使用的技术是子集系统的所谓不相交排序[S. Gao,B。Novick,K。Qiu,从Hall匹配定理到超立方体的最优路由,J。Comb。理论B 74(1998)291-301]。

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