On the pseudoachromatic number of join of graphs

Given an undirected graph G = (V, E), with vertex set V and edge set E, the pseudoachromatic number ψ(G) of the graph G is the maximum number of colors used to color the vertices in such a way that, for any given pair of colors i, j there exists an edge e = (u, v) ∈ E(G) such that u is colored i and v is colored j. In this paper we give a complete characterization of when the ψ of the join of any two graphs is the sum of the ψ of the two graphs.

Keywords:

• Pseudoachromatic Number
• Achromatic Number
• Join