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

Publikation: Beitrag in einer Fachzeitschrift › Artikel › Begutachtung

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.

Originalsprache	englisch
Seiten (von - bis)	117-126
Seitenumfang	10
Fachzeitschrift	Ars Mathematica Contemporanea
Jahrgang	18
Ausgabenummer	1
DOIs	https://doi.org/10.26493/1855-3974.1852.4F7
Publikationsstatus	Veröffentlicht - 1 Jan. 2020
Extern publiziert	Ja

ASJC Scopus subject areas

Theoretische Informatik
Algebra und Zahlentheorie
Geometrie und Topologie
Diskrete Mathematik und Kombinatorik

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10.26493/1855-3974.1852.4F7

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The distinguishing index of connected graphs without pendant edges

Abstract

ASJC Scopus subject areas

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