| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 420792 | Discrete Applied Mathematics | 2006 | 9 Pages |
For two vertices uu and vv in a strong digraph DD, the strong distance sd(u,v)sd(u,v) between uu and vv is the minimum size (the number of arcs) of a strong sub-digraph of DD containing uu and vv. For a vertex vv of DD, the strong eccentricity se(v)se(v) is the strong distance between vv and a vertex farthest from vv. The strong radius srad(D)srad(D) (resp. strong diameter sdiam(D)sdiam(D)) is the minimum (resp. maximum) strong eccentricity among the vertices of DD. The lower (resp. upper) orientable strong radius srad(G)srad(G) (resp. SRAD(G)SRAD(G)) of a graph G is the minimum (resp. maximum) strong radius over all strong orientations of G . The lower (resp. upper) orientable strong diameter sdiam(G)sdiam(G) (resp. SDIAM(G)SDIAM(G)) 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 kk-partite graphs, and give the upper orientable strong diameter and the bounds on the upper orientable strong radius of complete kk-partite graphs. We also find an error about the lower orientable strong diameter of complete bipartite graph Km,nKm,n 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 sdiam(Km,n)sdiam(Km,n).
