The distinguishing index of connected graphs without pendant edges

Wilfried Imrich, Rafał Kalinowski, Monika Pilsniak, Mariusz Wozniak

Research output: Contribution to journalArticlepeer-review

Abstract

We consider edge colourings, not necessarily proper. The distinguishing index D0(G) of a graph G is the least number of colours in an edge colouring that is preserved only by the identity automorphism. It is known that D0(G) ≤ ∆ for every countable, connected graph G with finite maximum degree ∆ except for three small cycles. We prove that D0(G) ≤ d∆e + 1 if additionally G does not have pendant edges.

Original languageEnglish
Pages (from-to)117-126
Number of pages10
JournalArs Mathematica Contemporanea
Volume18
Issue number1
DOIs
Publication statusPublished - 1 Jan 2020
Externally publishedYes

Keywords

  • Distinguishing index of a graph
  • Symmetry breaking

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Algebra and Number Theory
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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