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 language | English |
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Pages (from-to) | 117-126 |
Number of pages | 10 |
Journal | Ars Mathematica Contemporanea |
Volume | 18 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1 Jan 2020 |
Externally published | Yes |
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