Cayley graphs on abelian groups
Let A be an abelian group and let ι be the automorphism of A defined by: ι: a ↦ a −1 . A Cayley graph Γ = Cay( A,S ) is said to have an automorphism group as small as possible if Aut(Γ)=A⋊<ι>. In this paper, we show that almost all Cayley graphs on abelian groups have automorphism group as sma...
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| Published in | Combinatorica (Budapest. 1981) Vol. 36; no. 4; pp. 371 - 393 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.08.2016
Springer Nature B.V |
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| Abstract | Let
A
be an abelian group and let ι be the automorphism of
A
defined by: ι: a ↦ a
−1
. A Cayley graph Γ = Cay(
A,S
) is said to have an automorphism group
as small as possible
if Aut(Γ)=A⋊<ι>. In this paper, we show that almost all Cayley graphs on abelian groups have automorphism group as small as possible, proving a conjecture of Babai and Godsil. |
|---|---|
| AbstractList | Let A be an abelian group and let ι be the automorphism of A defined by: ι: a ↦ a−1. A Cayley graph Γ = Cay(A,S) is said to have an automorphism group as small as possible if Aut(Γ)=A⋊<ι>. In this paper, we show that almost all Cayley graphs on abelian groups have automorphism group as small as possible, proving a conjecture of Babai and Godsil. Let A be an abelian group and let ι be the automorphism of A defined by: ι: a ↦ a −1 . A Cayley graph Γ = Cay( A,S ) is said to have an automorphism group as small as possible if Aut(Γ)=A⋊<ι>. In this paper, we show that almost all Cayley graphs on abelian groups have automorphism group as small as possible, proving a conjecture of Babai and Godsil. |
| Author | Verret, Gabriel Spiga, Pablo Dobson, Edward |
| Author_xml | – sequence: 1 givenname: Edward surname: Dobson fullname: Dobson, Edward organization: Department of Mathematics and Statistics, Mississippi State University, Inštitut Andrej Marušic, University of Primorska – sequence: 2 givenname: Pablo surname: Spiga fullname: Spiga, Pablo organization: Departimento di Matematica Pura e Applicata, University of Milano-Bicocca – sequence: 3 givenname: Gabriel surname: Verret fullname: Verret, Gabriel email: gabriel.verret@uwa.edu.au organization: Centre for Mathematics of Symmetry and Computation, School of Mathematics and Statistics, The University of Western Australia, University of Primorska, FAMNIT |
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| Cites_doi | 10.1007/s10801-005-6903-3 10.1007/BF02773471 10.1016/j.ejc.2014.07.003 10.1515/jgt-2014-0015 10.1016/S0195-6698(82)80003-6 10.4153/CJM-1972-101-5 10.1090/gsm/092 10.1016/S0021-9800(68)80086-9 10.1006/jabr.1996.0220 10.1007/BF02107568 10.1007/978-3-642-61804-8 10.1017/S144678870003216X 10.1016/0021-8693(78)90259-4 10.1112/plms/pdr004 10.1007/b97433 10.1007/BF02579330 10.1090/memo/0432 10.26493/1855-3974.120.c55 10.26493/1855-3974.315.868 |
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| References | Xu (CR27) 1998; 182 Jabara, Spiga (CR14) 2013; 101 Babai (CR2) 1980; 11 Imrich (CR12) 1978 Suzuki (CR26) 1982 Godsil (CR10) 1981; 1 Leung, Man (CR17) 1998; 106 Dobson (CR7) 2010; 3 A. Evdokimov, Ponomarenko (CR8) 2002; 14 Isaacs (CR13) 2008 Nowitz, Watkins (CR24) 1972; 24 Yoshida (CR28) 1978; 52 Bhoumik, Dobson, Morris (CR4) 2014; 7 Casolo, Jabara, Spiga (CR5) 2014; 17 Li (CR18) 2005; 21 H. Conway, Curtis, Norton, Parker, Wilson (CR6) 1985 Leung, Man (CR16) 1996; 183 Liebeck, Praeger, Saxl (CR20) 1988; 44 CR25 Babai (CR1) 1978; 37 Godsil (CR9) 1981 Li, Zhang (CR19) 2011; 103 Morris, Spiga, Verret (CR22) 2015; 43 CR21 Hetzel (CR11) 1976 Kurzweil, Stellmacher (CR15) 2004 Babai, Godsil (CR3) 1982; 3 Nowitz (CR23) 1968; 4 J H. Conway (3136_CR6) 1985 K H Leung (3136_CR16) 1996; 183 L Babai (3136_CR1) 1978; 37 W Imrich (3136_CR12) 1978 C H Li (3136_CR18) 2005; 21 M W Liebeck (3136_CR20) 1988; 44 M Isaacs (3136_CR13) 2008 C D Godsil (3136_CR9) 1981 H Kurzweil (3136_CR15) 2004 C Casolo (3136_CR5) 2014; 17 S A. Evdokimov (3136_CR8) 2002; 14 D Hetzel (3136_CR11) 1976 L A Nowitz (3136_CR24) 1972; 24 L Babai (3136_CR3) 1982; 3 K H Leung (3136_CR17) 1998; 106 L A Nowitz (3136_CR23) 1968; 4 L Babai (3136_CR2) 1980; 11 C D Godsil (3136_CR10) 1981; 1 J Morris (3136_CR22) 2015; 43 MY Xu (3136_CR27) 1998; 182 M Suzuki (3136_CR26) 1982 E Dobson (3136_CR7) 2010; 3 3136_CR25 S Bhoumik (3136_CR4) 2014; 7 3136_CR21 C H Li (3136_CR19) 2011; 103 T Yoshida (3136_CR28) 1978; 52 E Jabara (3136_CR14) 2013; 101 |
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| Snippet | Let
A
be an abelian group and let ι be the automorphism of
A
defined by: ι: a ↦ a
−1
. A Cayley graph Γ = Cay(
A,S
) is said to have an automorphism group
as... Let A be an abelian group and let ι be the automorphism of A defined by: ι: a ↦ a−1. A Cayley graph Γ = Cay(A,S) is said to have an automorphism group as small... |
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| Title | Cayley graphs on abelian groups |
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