On the comparison of the distinguishing coloring and the locating coloring of graphs

Let G be a simple connected graph. Then chi L(G) and chi D(G) will denote the locating chromatic number and the distinguishing chromatic number of G, respectively. In this paper, we investigate a comparison between chi L(G) and chi D(G). In fact, we prove that chi D(G) \leq chi L(G). Moreover, we de...

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Bibliographic Details
Published inarXiv.org
Main Authors Korivand, M, Erfanian, A, Baskoro, Edy T
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 07.12.2021
Subjects
Coloring
Graphs
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Summary:Let G be a simple connected graph. Then chi L(G) and chi D(G) will denote the locating chromatic number and the distinguishing chromatic number of G, respectively. In this paper, we investigate a comparison between chi L(G) and chi D(G). In fact, we prove that chi D(G) \leq chi L(G). Moreover, we determine some types of graphs whose locating and distinguishing chromatic numbers are equal. Specially, we characteristic all graph G with the property that chi D(G)= chi L(G) = 3.
ISSN:2331-8422