Szczegóły publikacji
Opis bibliograficzny
Distinguishing arc-colourings of symmetric digraphs / Rafał KALINOWSKI, Monika PILŚNIAK, Magdalena PROROK // The Art of Discrete and Applied Mathematics [Dokument elektroniczny]. - Czasopismo elektroniczne ; ISSN 2590-9770. — 2023 — vol. 6 no. 2, s. 1-14, P2.04. — Wymagania systemowe: Adobe Reader. — Bibliogr. s. 13-14, Abstr. — Publikacja dostępna online od: 2022-11-15
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Dane bibliometryczne
| ID BaDAP | 143712 |
|---|---|
| Data dodania do BaDAP | 2022-11-16 |
| Tekst źródłowy | URL |
| DOI | 10.26493/2590-9770.1472.24b |
| Rok publikacji | 2023 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Creative Commons | |
| Czasopismo/seria | The Art of Discrete and Applied Mathematics |
Abstract
A symmetric digraph G→ is obtained from an undirected graph G by replacing each edge uv of G by a pair of opposite arcs -→ uv and -→ vu. An arc-colouring of a digraph is called distinguishing if the only automorphism preserving it is the identity. The least number of colours in a distinguishing arc-colouring, not necessarily proper, of G→ is called the distinguishing index D( G→ ). We study bounds for D( G→ ). For proper distinguishing arc-colourings, the least number of colours is called the distinguishing chromatic index of G→ . There are 15 possible types of proper arc-colourings of a digraph depending on the definition of adjacent arcs. In this paper we investigate distinguishing chromatic indices of G→ for the nine remaining types not considered in our two previous papers. We formulate several conjectures. © 2023 Art of Discrete and Applied Mathematics. All rights reserved.