Oriented diameter of the complete tripartite graph (III)

TL;DR

This paper determines the minimum possible diameter among all strong orientations of the complete tripartite graph K(3,p,q) for p ≥ 5, extending the understanding of oriented diameters in graph theory.

Contribution

It explicitly calculates the oriented diameter of K(3,p,q) for p ≥ 5, filling a gap in the existing literature on graph orientations.

Findings

Oriented diameter of K(3,p,q) for p ≥ 5 is explicitly determined.

Results extend previous knowledge on complete tripartite graphs.

Provides a comprehensive understanding of strong orientations in these graphs.

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.