Research confirms conjecture on oriented diameter for complete tripartite graphs, suggesting significant insights into graph theory.
Given a connected and bridgeless graph G, let D(G) be the set of all strong orientations of G, and define the oriented diameter of G to be ? (G) = min{diam(D) | D ? D(G)}. Rajasekaran and Sampathkumar (Filomat, 2015) conjectured f (K(2, p, q)) = 3 when p ? 5 and q > (p?p/2?). 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.
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Liu et al. (2025) studied this question.
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