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Graphs and Combinatorics

, Volume 30, Issue 6, pp 1469–1477 | Cite as

Edge-Distinguishing Index of a Graph

  • Rafał KalinowskiEmail author
  • Mariusz Woźniak
Open Access
Original Paper
  • 529 Downloads

Abstract

We introduce a concept of edge-distinguishing colourings of graphs. A closed neighbourhood of an edge \({e\in E(G)}\) is a subgraph N[e] induced by e and all edges adjacent to it. We say that a colouring c : E(G) → C does not distinguish two edges e 1 and e 2 if there exists an isomorphism φ of N[e 1] onto N[e 2] such that φ(e 1) = e 2 and φ preserves colours of c. An edge-distinguishing index of a graph G is the minimum number of colours in a proper colouring which distinguishes every two distinct edges of G. We determine the edge-distinguishing index for cycles, paths and complete graphs.

Keywords

Proper edge colouring Chromatic index Euler tours in multigraphs 

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Copyright information

© The Author(s) 2013

Open AccessThis article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

Authors and Affiliations

  1. 1.Department of Discrete MathematicsAGH University of Science and TechnologyKrakowPoland

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