Number theoretic designs for directed regular graphs of small diameter | Macquarie University ResearchOnline

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Title: Number theoretic designs for directed regular graphs of small diameter
Related: SIAM journal on discrete mathematics, Vol. 17, Issue 3, p.377-383
DOI: 10.1137/S0895480101396676
Publisher: Society for Industrial and Applied Mathematics
Date: 2004
FoR/RFCD Code(s): 080200 Computation Theory and Mathematics
Author/Creator: Banks, William D
Author/Creator: Conflitti, Alessandro
Author/Creator: Shparlinski, Igor E
Description: In 1989, F. R. K. Chung gave a construction for certain directed h-regular graphs of small diameter.Her construction is based on finite fields, and the upper bound on the diameter of these graphs is derived from bounds for certain very short character sums. Here we present two similar constructions that are based on properties of discrete logarithms and exponential functions in residue rings modulo a prime power. Accordingly, we use bounds for certain sums with additive and multiplicative characters to estimate the diameter of our graphs. We also give a third construction that avoids the use of bounds for exponential sums.
Description: 7 page(s)
Subject Keyword: 080200 Computation Theory and Mathematics
Subject Keyword: exponential sums
Subject Keyword: character sums
Subject Keyword: extremal problems
Subject Keyword: graphs
Resource Type: journal article
Organisation: Macquarie University. Dept. of Computing

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