Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4653467 | European Journal of Combinatorics | 2015 | 8 Pages |
Abstract
We also introduce the distinguishing chromatic index ÏDâ²(G) defined for proper edge-colourings of a graph G. A correlation with distinguishing vertices by colour walks introduced in Kalinowski et al. (2004) is shown. We prove that ÏDâ²(G)â¤Î(G)+1 except for four small graphs C4, K4, C6 and K3,3. It follows that each connected Class 2 graph G admits a minimal proper edge-colouring, i.e., with Ïâ²(G) colours, preserved only by the trivial automorphism.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
RafaÅ Kalinowski, Monika PilÅniak,