Number theoretic designs for directed regular graphs of small diameter
SIAM Journal on Discrete Mathematics, 2004•SIAM
In 1989, FRK 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 …
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 …
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.
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