Graph theory is an important part of algebraic graph theory,which was originally a discrete graph model established by chemists and physicists when solving a class of partial differential equations.Graph theory is mainly to use the methods and skills of matrix theory to solve the properties of graph matrices,so as to use these matrix properties to reflect some structural properties and topological properties of graphs.Graph G is an n-order diagram.The rank r(G)of graph G is defined as the rank of the adjacency matrix of graph G,and the vertex set of graphs G is V(G).The degree d(v)of vertex v is defined as the number of edges associated with vertex v,for any v∈V(G),have d(v)≤3,then the graph G is called a chemical graph.This paper had described the chemical graph of rank 6.