Oriented diameter of the complete tripartite graph

Abstract

Given a graph $G$, let $\mathbb{D}(G)$ be the set of all strong orientations of $G$, and define the oriented diameter of $G$ to be
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$f(G)=\min\{\diam(D)\mid D\in \mathbb{D}(G)\}$.
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Rajasekaran and Sampathkumar (Filomat, 2015) conjectured
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$f(\K(2,p,q))=3$ when $p\geqslant 5$ and $q>\binom{p}{\lfloor\frac{p}{2}\rfloor}$.
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In this paper, we confirm this conjecture. Combining with the results of Koh and Tan (Graphs and Combinatorics, 1996), the oriented diameter of complete tripartite graph $\K(2,p,q)$ is completely determined.