TY - JOUR
T1 - Number theoretic designs for directed regular graphs of small diameter
AU - Banks, William D.
AU - Conflitti, Alessandro
AU - Shparlinski, Igor E.
PY - 2004/1
Y1 - 2004/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=4344621106&partnerID=8YFLogxK
U2 - 10.1137/S0895480101396676
DO - 10.1137/S0895480101396676
M3 - Article
AN - SCOPUS:4344621106
SN - 0895-4801
VL - 17
SP - 377
EP - 383
JO - SIAM Journal on Discrete Mathematics
JF - SIAM Journal on Discrete Mathematics
IS - 3
ER -