\magnification=1200
\hsize=4in
\overfullrule=0pt
\input amssym
%\def\frac#1 #2 {{#1\over #2}}
\def\emph#1{{\it #1}}
\def\em{\it}
\nopagenumbers
\noindent
%
%
{\bf Debra L. Boutin}
%
%
\medskip
\noindent
%
%
{\bf Identifying Graph Automorphisms Using Determining Sets}
%
%
\vskip 5mm
\noindent
%
%
%
%
A set of vertices $S$ is a determining set for a graph $G$ if every
automorphism of $G$ is uniquely determined by its action on $S$. The
determining number of a graph is the size of a smallest determining
set. This paper describes ways of finding and verifying determining
sets, gives natural lower bounds on the determining number, and shows
how to use orbits to investigate determining sets. Further,
determining sets of Kneser graphs are extensively studied, sharp
bounds for their determining numbers are provided, and all Kneser
graphs with determining number $2$, $3,$ or $4$ are given.
\bye