Strongly self-centered orientation of complete [formula omitted]-partite graphs

Abstract

For two vertices u and v in a strong oriented graph D, the strong distance sd(u,v) between u and v is the minimum size (the number of arcs) of a strong sub-digraph of D containing u and v. For a vertex v of D, the strong eccentricity se(v) is the strong distance between v and a vertex farthest from v. The strong radius srad(D) is the minimum strong eccentricity among the vertices of D, and the strong diameter sdiam(D) is the maximum strong eccentricity among the vertices of D. An orientation D of a graph G is said to be a strongly self-centered orientation of G if srad(D)=sdiam(D). In this paper, we obtain some conditions for complete k-partite graphs to have strongly self-centered orientations. Our results generalize a result on tournaments in Chartrand et al. (1999).