Distance-regular graphs, MH-colourings and MLD-colourings. (English) Zbl 0887.05019
A minimal line-distinguishing colouring is a vertex colouring in which each pair of colours occurs exactly once on an edge. In this paper it is shown that the only bipartite distance-regular graphs of diameter three that have a minimal line-distinguishing colouring are the incidence graphs of complementary Hadamard designs.
Reviewer: C.Jagger (Cambridge)
MSC:
| 05C15 | Coloring of graphs and hypergraphs |
References:
| [1] | Brunton, B. E.; Wilson, B. J.; Griggs, T. S., Graphs which have \(n/2\)-minimal line-distinguishing colourings, (Proc. Combinatorics 92. Proc. Combinatorics 92, Discrete Math., 155 (1996)), 19-26 · Zbl 0858.05043 |
| [2] | Casse, L. R.A.; O’Keefe, C. M.; Wilson, B. J., Minimal harmoniously colourable designs, J. Combin. Designs, 2, 61-69 (1994) · Zbl 0843.05010 |
| [3] | Wilson, B. J., Minimal line distinguishing colourings in graphs, (Proc. Combinatorics 90. Proc. Combinatorics 90, Ann. Discrete Math., 52 (1992)), 549-558 · Zbl 0773.05050 |
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