Abstract
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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
