Oriented diameter of the complete tripartite graph (III)

Abstract

Given a bridgeless graph $G$, let $\mathbb{D}(G)$ be the set of all strong orientations of $G$, and define the oriented diameter $f(G)$ of $G$ to be the minimum of diameters $diam(D)$ among all the strong orientations $D\in \mathbb{D}(G)$, i.e., $f(G)=\min\{diam(D)\mid D\in \mathbb{D}(G)\}$. In this paper, we determine the oriented diameter of complete tripartite graph $K(3,p,q)$ for $p\geqslant 5$. Combining with the previous results, the oriented diameter of complete tripartite graph $K(3,p,q)$ are known.