Compact graphs and equitable partitions

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Let G be a graph with adjacency matrix A, and let Γ be the set of all permutation matrices which commute with A. We call G compact if every doubly stochastic matrix which commutes with A is a convex combination of matrices from Γ. We characterize the graphs for which S(A) = {I} and show that the automorphism group of a compact regular graph is generously transitive, i.e., given any two vertices, there is an automorphism which interchanges them. We also describe a polynomial time algorithm for determining whether a regular graph on a prime number of vertices is compact. © Elsevier Science Inc., 1997.




Godsil, C. D. (1997). Compact graphs and equitable partitions. Linear Algebra and Its Applications, 255(1–3), 259–266.

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