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On the diameter of the generalized undirected de Bruijn graphs UGB(n,m), n2 m ≤ n3

✍ Scribed by Jyhmin Kuo; Hung-Lin Fu

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
84 KB
Volume
52
Category
Article
ISSN
0028-3045

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✦ Synopsis

Abstract

The generalized de Bruijn digraph G~B~(n,m) is the digraph (V,A) where V = {0, 1,…,m − 1} and (i,j) ∈ A if and only if j ≡ i____n+α (mod m) for some α ∈ {0, 1, 2,…,n− 1}. By replacing each arc of G~B~(n,m) with an undirected edge and eliminating loops and multi‐edges, we obtain the generalized undirected de Bruijn graph U____G~B~(n,m). In this article, we prove that when 2__n__^2^ ≤ m ≤ n^3^ the diameter of U____G~B~(n,m) is equal to 3. We also show that for pairs (n,m) where n^2^ <m< 2__n__^2^ the diameter of U____G~B~(n,m) can be 2 or 3. © 2008 Wiley Periodicals, Inc. NETWORKS, 2008

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