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Diameters of finite upper half plane graphs

✍ Scribed by Angel, Jeff; Evans, Ronald

Publisher: John Wiley and Sons
Year: 1996
Tongue: English
Weight: 370 KB
Volume: 23
Category: Article
ISSN: 0364-9024
DOI: 10.1002/(sici)1097-0118(199610)23:2<129::aid-jgt4>3.0.co;2-v

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✦ Synopsis

Let GF(q) be a finite field of q elements. Let G denote the group of matrices M ( z , y) = (," y ) over GF(q) with y # 0. Fix an irreducible polynomial

For each a E G F ( q ) , let X , be the graph whose vertices are the q2 -q elements of G, with two vertices M ( z , y), M ( v , w) joined by an edge if and only if

The graphs X , with a $ ! (0, t2 -472) are (q + 1)-regular connected graphs which have received recent attention, as they've been shown to be Ramanujan graphs. We determine the diameter of these graphs X,.

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