Abstract
. Let d(D) (resp., d(G)) denote the diameter and r(D) (resp., r(G)) the radius of a digraph D (resp., graph G). Let G×H denote the cartesian product of two graphs G and H. An orientation D of G is said to be (r, d)-invariant if r(D)=r(G) and d(D)=d(G). Let {T i }, i=1,…,n, where n≥2, be a family of trees. In this paper, we show that the graph ∏ i =1 n T i admits an (r, d)-invariant orientation provided that d(T 1)≥d(T 2)≥4 for n=2, and d(T 1)≥5 and d(T 2)≥4 for n≥3.
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Received: July 30, 1997 Final version received: April 20, 1998
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Koh, K., Tay, E. On Optimal Orientations of Cartesian Products of Trees. Graphs Comb 17, 79–97 (2001). https://doi.org/10.1007/s003730170057
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DOI: https://doi.org/10.1007/s003730170057