Circulant example

1365 days ago by hthall

G = graphs.CirculantGraph(9,[1,3]) G 
       
show(G.adjacency_matrix()) 
       

                                
                            

                                
M = Matrix(ZZ, [[1, 1, 0, 5, 0, 0, -2, 0, 1], [0, 6, 0, 0, 3, 0, 2, 1, 4], [0, 0, 2, 0, 2, 1, 1, 0, 4], [0, 5, 1, 1, 4, 0, 2, 0, 5]]) show(M) 
       

                                
                            

                                
D = diagonal_matrix([1, 1, 1, -1]) show(D) 
       

                                
                            

                                
A = M.transpose() * D * M show(A) 
       

                                
                            

                                
G.is_isomorphic(Graph(A - diagonal_matrix(A.diagonal()))) 
       
True
True