Oriented diameter of the complete tripartite graph (II)

TL;DR

This paper determines the minimum possible diameters of strongly oriented complete tripartite graphs, specifically for the cases K(3,3,q) and K(3,4,q), advancing understanding of their directed properties.

Contribution

It provides the exact oriented diameters for K(3,3,q) and K(3,4,q), filling gaps in the knowledge of oriented diameters for these specific tripartite graphs.

Findings

Oriented diameter of K(3,3,q) determined

Oriented diameter of K(3,4,q) determined

Results aid in understanding the oriented diameter of K(3,p,q)

Abstract

For a graph $G$, let $\mathbb{D}(G)$ denote the set of all strong orientations of $G$, and the oriented diameter of $G$ is $f(G)=\min \{diam(D) \mid D \in \mathbb{D}(G)\}$, which is the minimum value of the diameters $diam(D)$ where $D \in \mathbb{D}(G)$. In this paper, we determine the oriented diameter of complete tripartite graphs $K(3,3, q)$ and $K(3,4, q)$, these are special cases that arise in determining the oriented diameter of $K(3, p, q)$.