Hidden symmetry in molecular graphs

Abstract

The concept of the Hamiltonian group of a graph is introduced to specify the full symmetry properties of the adjacency matrix (Hamiltonian operator). Three group theoretical rules and a new method are presented which allow the hidden symmetry of a graph to be systematically and rigorously investigated. Based on one subgroup of the Hamiltonian group, the hidden symmetry problem in an alternant molecular graph sharing doubly degenerate eigenvalues x=0 is solved in general.