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.
- 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