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On Cayley digraphs on nonisomorphic 2‐groups
Author(s) -
Kovács István,
Servatius Mary
Publication year - 2012
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.20625
Subject(s) - cayley graph , mathematics , combinatorics , automorphism , abelian group , vertex transitive graph , cayley's theorem , prime (order theory) , graph , cyclic group , discrete mathematics , voltage graph , line graph
A necessary and sufficient condition is given for two Cayley digraphs X 1 = Cay ( G 1 , S 1 ) and X 2 = Cay( G 2 , S 2 ) to be isomorphic, where the groups G i are nonisomorphic abelian 2‐groups, and the digraphs X i have a regular cyclic group of automorphisms. Our result extends that of Morris [J Graph Theory 3 (1999), 345–362] concerning p ‐groups G i , where p is an odd prime. Copyright © 2011 Wiley Periodicals, Inc. J Graph Theory
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