\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 Xueliang Li and Yan Liu}
%
%
\medskip
\noindent
%
%
{\bf Nonexistence of Triples of Nonisomorphic Connected Graphs with Isomorphic Connected $P_3$-graphs}
%
%
\vskip 5mm
\noindent
%
%
%
%
In the paper ``Broersma and Hoede, {\it Path graphs}, J. Graph Theory
{\bf 13} (1989) 427-444", the authors asked a problem whether there is
a triple of mutually nonisomorphic connected graphs which have an
isomorphic connected $P_3$-graph. In this paper, we show that there is
no such triple, and thus completely solve this problem.



\bye

.
