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Diameter and mean distance of bipartite digraphs related to plane tessellations. (English) Zbl 0711.05023

Authors’ summary: “It is possible to associate plane tessellations with certain digraphs over the set of vertices \(V={\mathbb{Z}}/n{\mathbb{Z}}\). This association enables a geometrical, and in general simpler, approach to their study. We use this relation for obtaining the maximum order, minimum diameter and minimum mean distance of a family of bipartite digraphs of degree two. The results found improve those known for similar families of digraphs with the same degree.”
Reviewer: G.Chaty

MSC:

05C20 Directed graphs (digraphs), tournaments
05B45 Combinatorial aspects of tessellation and tiling problems
05C12 Distance in graphs
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