Graphs, groups and polytopes
With each eigenspace of the adjacency matrix A of a graph X there is an associated convex polytope. Any automorphism of X induces an orthogonal transformation of this polytope onto itself. These observations are used to obtain information on the relation between the automorphism group of X and the multiplicities of the eigenvalues of A. This approach yields new results on this topic as well as improvements of previously known ones.
KeywordsNormal Subgroup Weight Vector Automorphism Group Adjacency Matrix Coxeter Group
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