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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1104,
author = {Shannon L. Fitzpatrick and Richard J. Nowakowski},
title = {The strong isometric dimension of finite reflexive graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {20},
year = {2000},
pages = {23-38},
zbl = {0966.05026},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1104}
}
Shannon L. Fitzpatrick; Richard J. Nowakowski. The strong isometric dimension of finite reflexive graphs. Discussiones Mathematicae Graph Theory, Tome 20 (2000) pp. 23-38. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1104/
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