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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Maxwell Ndognkon Manga
Department of Computer Sciences, Faculty of Sciences, University of Yaound\'e 1, P.O. Box 812 Yaound\'e, Cameroon
Electrical & Electronics Engineering

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Coloring properties of corona products in signed graphs Pie Desire Ebode Atangana; Maxwell Ndognkon Manga; Erick Patrick Zobo
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 14, No 2 (2026): 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.2026.14.2.4

Abstract

This paper studies coloring and circular coloring of signed graphs. A signed graph is a graph together with a signature that assigns to each edge a sign which is either positive or negative. This paper studies coloring properties of corona products of signed graphs, including vertex corona product, edge corona product, neighbourhood corona product. Assume (G, σ) and (H, τ) are two signed graphs. The vertex corona product, edge corona product and neighborhood corona product of (G, σ) and (H, τ) are denoted by (G ⊙ H, σ ⊙ τ), (G ⋄ H, σ ⋄ τ), and (G ⋆ H, σ ⋆ τ), respectively. We obtain the following upper bounds for their chromatic numbers: χ(G ⊙ H, σ ⊙ τ) ≤ max{χ(G, σ), χ(H, τ) + 2}, χ(G ⋄ H, σ ⋄ τ) ≤ max{χ(G, σ), χ(H, τ) + 4}, and χ(G ⋆ H, σ ⋆ τ) ≤ max{χ(G, σ), χ(H, τ) + 2(Δ(G) + 1)}. Then we study circular coloring of corona products of graphs, and obtained the following upper bounds: χc(G ⊙ H, σ ⊙ τ) ≤ max{χc(G, σ), χc(H, τ) + 4}, χc(G ⋄ H, σ ⋄ τ) ≤ max{χc(G, σ), χc(H, τ) + 8}, and χc(G ⋆ H, σ ⋆ τ) ≤ max{χc(G, σ), χc(H, τ) + 4(Δ(G) + 1)}. We shall show that the upper bound for the circular chromatic number of vertex corona product is attained, by constructing signed Paley graph that achieves this upper bound.
Co-Authors Erick Patrick Zobo Pie Desire Ebode Atangana