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Minimizing and maximizing the diameter in orientations of graphs

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Abstract

For a graph G, letG′(G″) denote an orientation ofG having maximum (minimum respectively) finite diameter. We show that the length of the longest path in any 2-edge connected (undirected) graph G is precisely diam(G′). LetK(m l ,m 2,...,m n) be the completen-partite graph with parts of cardinalitiesm 1 m2, …,m n . We prove that ifm 1 = m2 = … =m n = m,n ≥ 3, then diam(K″(m1,m2,...,mn)) = 2, unless m=1 andn = 4.

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  1. Raymond and Beverly Sackler Faculty of Exact Sciences, School of Mathematical Sciences, Tel Aviv University, 69978, Ramat-Aviv, Israel

    G. Gutin

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  1. G. Gutin
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Gutin, G. Minimizing and maximizing the diameter in orientations of graphs. Graphs and Combinatorics 10, 225–230 (1994). https://doi.org/10.1007/BF02986669

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  • DOI: https://doi.org/10.1007/BF02986669

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