Short containers in Cayley graphs

Authors:
Shuhong Gao;D. Frank Hsu
Affiliations:
Department of Mathematical Sciences, Clemson University, Clemson, SC 29634, USA;Department of Computer and Information Science, 113 West 60th Street, LL 813, Fordham University, New York, NY 10023, USA and DIMACS, Rutgers University, Piscataway, NJ 08854-8018, USA
Venue:
Discrete Applied Mathematics
Year:
2009

Citing 12
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Abstract

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 Qiu [S. Gao, B. Novick, K. Qiu, From Hall's matching theorem to optimal routing on hypercubes, J. Comb. Theory B 74 (1998) 291-301].