Quaternions and equidistributive eigenvectors of symmetric graphs. (English) Zbl 0936.05069
Summary: Equidistributive eigenvectors of the adjacency matrix of a symmetric graph have equal weight on equivalent vertices. Real and complex coefficients are in general insufficient to achieve this property for all components of a degenerate manifold of an arbitrary graph. Quaternionic vector coefficients are shown to be necessary for equidistributivity of four- and fivefold degeneracies of the dodecahedron. Possible physical realisations of the equidistributivity property in molecular cages are also considered.
MSC:
05C50 | Graphs and linear algebra (matrices, eigenvalues, etc.) |
05C25 | Graphs and abstract algebra (groups, rings, fields, etc.) |
05C90 | Applications of graph theory |