The number of distinguishing colorings of a Cartesian product graph

A vertex coloring is called distinguishing if the identity is the only automorphism that can preserve it. The distinguishing threshold θ(G) of a graph G is the minimum number of colors k required that any arbitrary k-coloring of G is distinguishing. In this paper, we calculate the distinguishing thr...

Full description

Saved in:
Bibliographic Details
Published inQuaestiones mathematicae Vol. 47; no. 4; pp. 921 - 931
Main Authors Alikhani, Saeid, Shekarriz, Mohammad H.
Format Journal Article
LanguageEnglish
Published Grahamstown Taylor & Francis 26.04.2024
Taylor & Francis Ltd
Subjects
Automorphisms
Cartesian coordinates
Cartesian product
Distinguishing coloring
distinguishing threshold
Graph coloring
holo-graphic coloring
Mathematical analysis
Online AccessGet full text

Cover

More Information
Summary:A vertex coloring is called distinguishing if the identity is the only automorphism that can preserve it. The distinguishing threshold θ(G) of a graph G is the minimum number of colors k required that any arbitrary k-coloring of G is distinguishing. In this paper, we calculate the distinguishing threshold of a Cartesian product graph. Moreover, we calculate the number of non-equivalent distinguishing colorings of grids.
ISSN:1607-3606
1727-933X
DOI:10.2989/16073606.2023.2274580