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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Jabulani Phakathi
School of Mathematics, University of the Witwatersrand, Johannesburg, South Africa
Electrical & Electronics Engineering

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Symmetric colorings of G × Z_2 Jabulani Phakathi; Yevhen Zelenyuk; Yuliya Zelenyuk
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 11, No 2 (2023): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2023.11.2.3

Abstract

Let G be a finite group and let r ∈ N. An r-coloring of G is any mapping χ : G → {1, …, r}. A coloring χ is symmetric if there is g ∈ G such that χ(gx−1g)=χ(x) for every x ∈ G. We show that if f(r) is the polynomial representing the number of symmetric r-colorings of G, then the number of symmetric r-colorings of G × Z2 is f(r2).
Co-Authors Yevhen Zelenyuk Yuliya Zelenyuk