Automorphism groups of circulants and adjoint matrices of graphs

Autor:	V. E. Tarakanov
Rok vydání:	1999
Předmět:	Combinatorics p-group Discrete mathematics Group isomorphism Inner automorphism Symmetric group General Mathematics Quaternion group Outer automorphism group General linear group Graph automorphism Mathematics
Zdroj:	Mathematical Notes. 65:335-343
ISSN:	1573-8876 0001-4346
Popis:	To a graph (or a digraph) Γ we assign two matricesN(A) andN(−1)(A) of inner products of the vector rows and of the vector columns, respectively, of the adjacency matrix of Γ; these matrices are said to be adjoint. We develop an approach to the study of the automorphism groups AutCn of the circulantsCn onn vertices by means of adjoint matrices. A necessity test for the isomorphism of two circulants in terms of the matrixN(A) is obtained (Theorem 1). With the help of this test, certain classes of circulantsCn for which the group AutCn is isomorphic to the cyclic group or to the dihedral group are singled out (Theorem 2). As an application, we give the classification of the circulantsCn of degreem=4 and, for the case in whichn is prime, present an explicit description of their automorphism groups (Theorem 3).
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::eea9e3c8e22253af7f5c44964803f431 https://doi.org/10.1007/bf02675076 Zobrazit plný text záznamu Full text from SpringerLink