The distinguishing index of connected graphs without pendant edges

Wilfried Imrich; Rafał Kalinowski; Monika Pilsniak; Mariusz Wozniak

doi:10.26493/1855-3974.1852.4F7

The distinguishing index of connected graphs without pendant edges

Wilfried Imrich, Rafał Kalinowski, Monika Pilsniak, Mariusz Wozniak

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	117-126
Number of pages	10
Journal	Ars Mathematica Contemporanea
Volume	18
Issue number	1
DOIs	https://doi.org/10.26493/1855-3974.1852.4F7
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

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10.26493/1855-3974.1852.4F7

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The distinguishing index of connected graphs without pendant edges

Abstract

Keywords

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