# DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

# IMPACT FACTOR 2018: 0.741

SCImago Journal Rank (SJR) 2018: 0.763

Rejection Rate (2018-2019): c. 84%

# Discussiones Mathematicae Graph Theory

## THE STRONG ISOMETRIC DIMENSION OF FINITE REFLEXIVE GRAPHS

 Shannon L. Fitzpatrick University of Victoria Victoria, British Columbia Richard J. Nowakowski Dalhousie University Halifax, Nova Scotia

## 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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