Let G = (V, A) be an oriented graph. An oriented k-coloring of G is a partition of V into k subsets such that there are no two adjacent vertices belonging to the same subset, and all the arcs between a pair of subsets have the same orientation. The oriented chromatic number Xo(G) of G is the smallest k, such that G admits an oriented k-coloring. Oriented chromatic number of product of graphs were widely studied, but the disjoint union has not being considered. In this article we study oriented coloring for the disjoint union of graphs. We establish the exact values of the union: of two complete graphs, of one complete with a forest graph, and of one complete and one cycle. And we use those results to characterize the class of graphs G with Xo(G) <= 3. We evaluate, as far as we know for the first time, the value of Xo(Wn) and we yield with this value an upper bound for the union of one complete and one wheel graph Wn.

https://link.springer.com/chapter/10.1007/978-3-030-79987-8_14