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Chung, Fan R. K.; Sternberg, Shlomo

Laplacian and vibrational spectra for homogeneous graphs. (English) Zbl 0768.05049

J. Graph Theory 16, No. 6, 605-627 (1992).
Authors’ summary: A homogeneous graph is a graph together with a group that acts transitively on vertices as symmetries 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.
Reviewer: S.C.Althoen (Flint)

Cited in 12 Documents

MSC:

05C25 Graphs and abstract algebra (groups, rings, fields, etc.)

Keywords:

Laplacian; vibrational spectra; homogeneous graphs; eigenvalues; group representation theory; gauge theory
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References:

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