Lower and upper orientable strong radius and strong diameter of complete k-partite graphs Original Research Article

For two vertices image and image in a strong digraph image, the strong distance image between image and image is the minimum size (the number of arcs) of a strong sub-digraph of image containing image and image. For a vertex image of image, the strong eccentricity image is the strong distance between image and a vertex farthest from image. The strong radius image (resp. strong diameter image) is the minimum (resp. maximum) strong eccentricity among the vertices of image. The lower (resp. upper) orientable strong radius image (resp. image) of a graph G is the minimum (resp. maximum) strong radius over all strong orientations of G. The lower (resp. upper) orientable strong diameter image (resp. image) of a graph G is the minimum (resp. maximum) strong diameter over all strong orientations of G. In this paper, we determine the lower orientable strong radius and diameter of complete image-partite graphs, and give the upper orientable strong diameter and the bounds on the upper orientable strong radius of complete image-partite graphs. We also find an error about the lower orientable strong diameter of complete bipartite graph image given in [Y.-L. Lai, F.-H. Chiang, C.-H. Lin, T.-C. Yu, Strong distance of complete bipartite graphs, The 19th Workshop on Combinatorial Mathematics and Computation Theory, 2002, pp. 12–16], and give a rigorous proof of a revised conclusion about image.