Shannon-Vizing-type problems concerning the upper bound for a distance chromatic index of multigraphs G in terms of the maximum degree Δ(G) are studied. Conjectures generalizing those related to the strong chromatic index are presented. The chromatic d-index and chromatic d-number of paths, cycles, trees and some hypercubes are determined. Among hypercubes, however, the exact order of their growth is found.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1010,
author = {Zdzis\l aw Skupie\'n},
title = {Some maximum multigraphs and edge/vertex distance colourings},
journal = {Discussiones Mathematicae Graph Theory},
volume = {15},
year = {1995},
pages = {89-106},
zbl = {0833.05036},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1010}
}
Zdzisław Skupień. Some maximum multigraphs and edge/vertex distance colourings. Discussiones Mathematicae Graph Theory, Tome 15 (1995) pp. 89-106. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1010/
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