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Discussiones Mathematicae Graph Theory 15(1) (1995) 89-106
DOI: https://doi.org/10.7151/dmgt.1010

SOME MAXIMUM MULTIGRAPHS AND EDGE/VERTEX DISTANCE COLOURINGS

Zdzisław Skupień

Institute of Math. AGH
al. Mickiewicza 30, 30-059 Krakಷ, Poland
e-mail: skupien@uci.agh.edu.pl

Abstract

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.

Keywords: (strong) chromatic index, chromatic number, matching, hypercube, error-correcting code, asymptotics

1991 Mathematics Subject Classification: 05C15, 05C35, 94B05

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