Laplacian and vibrational spectra for homogeneous graphs

A homogeneous graph is a graph togerther with a group that acts transitively on vertices as symmertries of the graph. We consider Laplacians of homogeneous graphs and generalizations of Laplacians whose eigenvalues can be associated with various equilibria of forces in molecules (such as vibrational modes of buckyballs). Methods are given for calculating such eigenvalues by combining concepts and techniques in group representation theory, gauge theory and graph theory.