  The Travelling Salesman Problem (TSP), finding a minimal weighted Hamilton
cycle in a graph, is a typical problem in operation research and combinatorial
optimization. In this paper, based on some novel properties on Hamilton graphs,
we present a precise algorithm for finding a minimal weighted Hamilton cycle in
a non-metric and symmetric graph with time complexity of \textit{O}(|E(G)|^3) ,
where |E(G)| is the size of graph G.
