 
Summary: Representation Numbers of Complete Multipartite
Graphs
Reza Akhtar
Dept. of Mathematics
Miami University, Oxford, OH 45056, USA
reza@calico.mth.muohio.edu
Anthony B. Evans
Dept. of Mathematics and Statistics
Wright State University, Dayton, OH 45435, USA
Anthony.Evans@wright.edu
Dan Pritikin
Dept. of Mathematics
Miami University, Oxford, OH 45056, USA
pritikd@muohio.edu
September 16, 2010
Abstract
A graph G has a representation modulo r if there exists an injective map
f : V (G) # {0, 1, ..., r  1} such that vertices u and v are adjacent if and only
if f(u)  f(v) is relatively prime to r. The representation number rep(G) is
the smallest r such that G has a representation modulo r. Following earlier
