Coloring properties of corona products in signed graphs

Pie Desire Ebode Atangana (Department of Mathematics, Faculty of sciences, University of Yaounde 1, Yaounde, Cameroon)
Maxwell Ndognkon Manga (Department of Computer Sciences, Faculty of Sciences, University of Yaound\'e 1, P.O. Box 812 Yaound\'e, Cameroon)
Erick Patrick Zobo (Department of Computer Sciences, Higher Teacher's Training College, University of Yaounde 1, Cameroon. Laboratory of Computer Science and Educational Technologies (LITE), Yaounde, P.O. Box 47, Cameroon.)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 14, No 2 (2026): Electronic Journal of Graph Theory and Applications

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.