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Discussiones Mathematicae Graph Theory 20(1) (2000) 23-38
DOI: https://doi.org/10.7151/dmgt.1104

THE STRONG ISOMETRIC DIMENSION OF FINITE REFLEXIVE GRAPHS

Abstract

The strong isometric dimension of a reflexive graph is related to its injective hull: both deal with embedding reflexive graphs in the strong product of paths. We give several upper and lower bounds for the strong isometric dimension of general graphs; the exact strong isometric dimension for cycles and hypercubes; and the isometric dimension for trees is found to within a factor of two.

Keywords: isometric, embedding, strong product, injective hull, paths, distance, metric.

1991 Mathematics Subject Classification: 05C12, 05C75.

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Received 30 November 1998
Revised 13 December 1999

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