Optimal strong (κ,d)-orientation of complete k-partite graphs

  • Authors:

  • Huifang Miao;Xiaofeng Guo

  • Affiliations:

  • Department of Communication Engineering, Xiamen University, Xiamen Fujian 361005, PR China;School of Mathematical Sciences, Xiamen University, Xiamen Fujian 361005, PR China

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2009

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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 diameter sdiam(D) is the maximum strong eccentricity among the vertices of D. The lower orientable strong diameter sdiam(G) of a graph G is the minimum strong diameter over all strong orientations of G. An orientation D of a graph G is said to be an optimal strong (@k,d)-orientation of G if @k(D)=@?@k(G)/2@? and sdiam(D)=sdiam(G), where @k(D) (resp. @k(G)) is the strong connectivity of D (resp. connectivity of G). In this paper, we will show that each complete k-partite graph has an optimal strong (@k,d)-orientation.