The isomorphism problem for circulant graphs via Schur ring theory
نویسندگان
چکیده
This paper concerns the applications of Schur ring theory to the isomorphism problem of circulant graphs (Cayley graphs over cyclic groups). A digest of the most important facts about Schur rings presented in the first sections provides the reader with agentie self-eontained introduction to this area. The developed machinery allows us to give proofs of two eonjectures (Zibin' 1975 and Toida 1977) about necessary conditions on isomorphisms of the cireulants. These new results together with a few new proofs of some known facts show the feasibility of the teehnique of Schur rings in algebraic combinatorics. The eoncluding section contains a short historical and bibliographical survey of various results related to the isomorphism problem for Cayley graphs.
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