DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

Journal Impact Factor (JIF 2022): 0.7

5-year Journal Impact Factor (2022): 0.7

CiteScore (2022): 1.9

SNIP (2022): 0.902

Discussiones Mathematicae Graph Theory

Article in press

Authors:

S. Gravier

Sylvain Gravier

UGA-CNRS, Institut Fourier, FED Maths `a Modeler

email: sylvain.gravier@univ-grenoble-alpes.fr

H. Signargout

Hippolyte Signargout

UGA-CNRS, Institut Fourier, FED Maths a Modeler
12 ENS de Lyon, Departement d'Informatique

email: hippolyte.signargout@univ-grenoble-alpes.fr

S. Slimani

Souad Slimani

University of Sciences and Technology Houari Boumediene USTHB

email: sslimani@usthb.dz

0000-0001-9704-0217

Title:

Optimal adjacent vertex-distinguishing edge-colorings of circulant graphs

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Source:

Discussiones Mathematicae Graph Theory

Received: 2023-01-03 , Revised: 2023-04-20 , Accepted: 2023-04-20 , Available online: 2023-07-27 , https://doi.org/10.7151/dmgt.2508

Abstract:

A $k$-proper edge-coloring of a graph $G$ is called adjacent vertex-distinguishing if any two adjacent vertices are distinguished by the set of colors appearing in the edges incident to each vertex. The smallest value $k$ for which $G$ admits such coloring is denoted by $\chi^\prime _a(G)$. We prove that $\chi^\prime_a(G)=2R+1$ for most circulant graphs $C_n([ [1,R] ])$.

Keywords:

proper edge-coloring, circulant graph, distinguishing vertices, adjacent vertex-distinguishing, chromatic number

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