Graph Operations And Minimal Cycle Bases Of Graphs

Based on the situation in the plane,we show how the operations of 2-connected simple graphs influence the structure of minimal cycle bases. The main results are based on the following conditions:1 .Two 2-connected simple planar graphs intersect at unique point2.Two 2-connected simple planar graphs intersect at two points3.Two 2-connected simple planar graphs intersect at unique pathAs its application,basing on the main theory about the structure of minimal cycle bases of LEW-embedding graphs in the projective plane,as its application,we count the number of minimal cycle bases of a triangulation in projective plane.