Optimal orientations of subgraphs of complete bipartite graphs

Document Type : National Conference on Labelings and Decompositions of Graphs


1 Assistant Professor Department of mathematics Annamalai University Annamalainagar 608002

2 Research Scholar, Department of Mathematics, Annamalai University, Annamalainagar 608 002

3 Mathematics Section, FEAT, Annamalai University Annamalainagar 6008002


For a graph $G,$ let $\mathscr{D}(G)$ be the set of all strong digraphs $D$ obtained by the orientations of $G.$ The orientation number of $G$ is $\stackrel{\rightarrow}{d}\!\!(G)\,=$ min $\{d(D)\,|\,D\,\in\,\mathscr{D}(G)\},$ where $d(D)$ denotes the diameter of the digraph $D.$ In this paper‎, ‎we determine the orientation number for some subgraphs of complete bipartite graphs‎.


Main Subjects

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  • Receive Date: 13 September 2013
  • Revise Date: 24 February 2014
  • Accept Date: 25 February 2014
  • Published Online: 01 March 2015