A graph-theoretical method for stepwise factorisation of symmetric graphs for simultaneous determination of eigenvectors and eigenvalues

A simple pictorial algorithm for factorisation of symmetric chemical graphs (weighted and unweighted) leading to simultaneous determination of their eigenvalues and eigenvectors has been devised. The method does not require group-theoretical techniques (viz. identification of the point group of the species under study, formation of symmetryadopted linear combinations using character tables etc.). It requires consideration of only one symmetry element, e.g., a reflection plane and is based on elementary row and column operations which keep the secular determinant of the adjacency matrix unchanged (except possibly for a multiplicative constant).