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Laplacian and vibrational spectra for homogeneous graphs
Author(s) -
Chung Fan R. K.,
Sternberg Shlomo
Publication year - 1992
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190160607
Subject(s) - mathematics , homogeneous , spectral graph theory , eigenvalues and eigenvectors , combinatorics , graph , laplacian matrix , integral graph , laplace operator , line graph , discrete mathematics , voltage graph , quantum mechanics , physics , mathematical analysis
Abstract 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.