Study and application of transverse mining and longitudinal stripping

Optimization of rectilinear extensions of 4-regular graphs;

The determination of minimum bends in a rectilinear extension of a graph has been solved with effective algorithm.

This article discusses mainly four kinds of 4-regular graphs,gives a minimum bend number rectilinear extension for such a graph with any order,and provides the relation between its order and the minimum bend number.

In this paper , a generalized algorithm is provided to extend a 4regular graph to another 4regular graph through base rectilinear extension, through which the base rectilinear extension with the minimum total number of bends of the extended 4regular graph is naturally obtained from .