Non-normal edge-transitive directed Cayley graphs of abelian groups

For a group G, and a subset S of G such that $ 1_{G} $ ∉ S, let X = Cay(G,S) be the corresponding Cayley graph. Then X is said to be normal edge transitive if NAut(X)(G) is transitive on edges. In this paper, we determine all connected directed Cayley graphs of finite abelian groups with valency at...
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Gespeichert in:

Autor*in:	Alaeiyan, Mehdi [verfasserIn] Mirzajani, Javad [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2013

Schlagwörter:	Cayley graph Vertex transitive Edge transitive Normal edge transitive Normal graph Automorphism group

Übergeordnetes Werk:	Enthalten in: Mathematical sciences - Tehran : Springer, 2007, 7(2013), 1 vom: 11. Feb.
Übergeordnetes Werk:	volume:7 ; year:2013 ; number:1 ; day:11 ; month:02

Links:	Volltext

DOI / URN:	10.1186/2251-7456-7-7

Katalog-ID:	SPR032840861

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allfields	10.1186/2251-7456-7-7 doi (DE-627)SPR032840861 (SPR)2251-7456-7-7-e DE-627 ger DE-627 rakwb eng 510 ASE Alaeiyan, Mehdi verfasserin aut Non-normal edge-transitive directed Cayley graphs of abelian groups 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier For a group G, and a subset S of G such that $ 1_{G} $ ∉ S, let X = Cay(G,S) be the corresponding Cayley graph. Then X is said to be normal edge transitive if NAut(X)(G) is transitive on edges. In this paper, we determine all connected directed Cayley graphs of finite abelian groups with valency at most 3 which are normal edge transitive but not normal. AMS 05C10; 05C25 Cayley graph (dpeaa)DE-He213 Vertex transitive (dpeaa)DE-He213 Edge transitive (dpeaa)DE-He213 Normal edge transitive (dpeaa)DE-He213 Normal graph (dpeaa)DE-He213 Automorphism group (dpeaa)DE-He213 Mirzajani, Javad verfasserin aut Enthalten in Mathematical sciences Tehran : Springer, 2007 7(2013), 1 vom: 11. Feb. (DE-627)665433077 (DE-600)2620704-7 2251-7456 nnns volume:7 year:2013 number:1 day:11 month:02 https://dx.doi.org/10.1186/2251-7456-7-7 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 7 2013 1 11 02
spelling	10.1186/2251-7456-7-7 doi (DE-627)SPR032840861 (SPR)2251-7456-7-7-e DE-627 ger DE-627 rakwb eng 510 ASE Alaeiyan, Mehdi verfasserin aut Non-normal edge-transitive directed Cayley graphs of abelian groups 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier For a group G, and a subset S of G such that $ 1_{G} $ ∉ S, let X = Cay(G,S) be the corresponding Cayley graph. Then X is said to be normal edge transitive if NAut(X)(G) is transitive on edges. In this paper, we determine all connected directed Cayley graphs of finite abelian groups with valency at most 3 which are normal edge transitive but not normal. AMS 05C10; 05C25 Cayley graph (dpeaa)DE-He213 Vertex transitive (dpeaa)DE-He213 Edge transitive (dpeaa)DE-He213 Normal edge transitive (dpeaa)DE-He213 Normal graph (dpeaa)DE-He213 Automorphism group (dpeaa)DE-He213 Mirzajani, Javad verfasserin aut Enthalten in Mathematical sciences Tehran : Springer, 2007 7(2013), 1 vom: 11. Feb. (DE-627)665433077 (DE-600)2620704-7 2251-7456 nnns volume:7 year:2013 number:1 day:11 month:02 https://dx.doi.org/10.1186/2251-7456-7-7 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 7 2013 1 11 02
allfields_unstemmed	10.1186/2251-7456-7-7 doi (DE-627)SPR032840861 (SPR)2251-7456-7-7-e DE-627 ger DE-627 rakwb eng 510 ASE Alaeiyan, Mehdi verfasserin aut Non-normal edge-transitive directed Cayley graphs of abelian groups 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier For a group G, and a subset S of G such that $ 1_{G} $ ∉ S, let X = Cay(G,S) be the corresponding Cayley graph. Then X is said to be normal edge transitive if NAut(X)(G) is transitive on edges. In this paper, we determine all connected directed Cayley graphs of finite abelian groups with valency at most 3 which are normal edge transitive but not normal. AMS 05C10; 05C25 Cayley graph (dpeaa)DE-He213 Vertex transitive (dpeaa)DE-He213 Edge transitive (dpeaa)DE-He213 Normal edge transitive (dpeaa)DE-He213 Normal graph (dpeaa)DE-He213 Automorphism group (dpeaa)DE-He213 Mirzajani, Javad verfasserin aut Enthalten in Mathematical sciences Tehran : Springer, 2007 7(2013), 1 vom: 11. Feb. (DE-627)665433077 (DE-600)2620704-7 2251-7456 nnns volume:7 year:2013 number:1 day:11 month:02 https://dx.doi.org/10.1186/2251-7456-7-7 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 7 2013 1 11 02
allfieldsGer	10.1186/2251-7456-7-7 doi (DE-627)SPR032840861 (SPR)2251-7456-7-7-e DE-627 ger DE-627 rakwb eng 510 ASE Alaeiyan, Mehdi verfasserin aut Non-normal edge-transitive directed Cayley graphs of abelian groups 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier For a group G, and a subset S of G such that $ 1_{G} $ ∉ S, let X = Cay(G,S) be the corresponding Cayley graph. Then X is said to be normal edge transitive if NAut(X)(G) is transitive on edges. In this paper, we determine all connected directed Cayley graphs of finite abelian groups with valency at most 3 which are normal edge transitive but not normal. AMS 05C10; 05C25 Cayley graph (dpeaa)DE-He213 Vertex transitive (dpeaa)DE-He213 Edge transitive (dpeaa)DE-He213 Normal edge transitive (dpeaa)DE-He213 Normal graph (dpeaa)DE-He213 Automorphism group (dpeaa)DE-He213 Mirzajani, Javad verfasserin aut Enthalten in Mathematical sciences Tehran : Springer, 2007 7(2013), 1 vom: 11. Feb. (DE-627)665433077 (DE-600)2620704-7 2251-7456 nnns volume:7 year:2013 number:1 day:11 month:02 https://dx.doi.org/10.1186/2251-7456-7-7 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 7 2013 1 11 02
allfieldsSound	10.1186/2251-7456-7-7 doi (DE-627)SPR032840861 (SPR)2251-7456-7-7-e DE-627 ger DE-627 rakwb eng 510 ASE Alaeiyan, Mehdi verfasserin aut Non-normal edge-transitive directed Cayley graphs of abelian groups 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier For a group G, and a subset S of G such that $ 1_{G} $ ∉ S, let X = Cay(G,S) be the corresponding Cayley graph. Then X is said to be normal edge transitive if NAut(X)(G) is transitive on edges. In this paper, we determine all connected directed Cayley graphs of finite abelian groups with valency at most 3 which are normal edge transitive but not normal. AMS 05C10; 05C25 Cayley graph (dpeaa)DE-He213 Vertex transitive (dpeaa)DE-He213 Edge transitive (dpeaa)DE-He213 Normal edge transitive (dpeaa)DE-He213 Normal graph (dpeaa)DE-He213 Automorphism group (dpeaa)DE-He213 Mirzajani, Javad verfasserin aut Enthalten in Mathematical sciences Tehran : Springer, 2007 7(2013), 1 vom: 11. Feb. (DE-627)665433077 (DE-600)2620704-7 2251-7456 nnns volume:7 year:2013 number:1 day:11 month:02 https://dx.doi.org/10.1186/2251-7456-7-7 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 7 2013 1 11 02
language	English
source	Enthalten in Mathematical sciences 7(2013), 1 vom: 11. Feb. volume:7 year:2013 number:1 day:11 month:02
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topic_facet	Cayley graph Vertex transitive Edge transitive Normal edge transitive Normal graph Automorphism group
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author	Alaeiyan, Mehdi
spellingShingle	Alaeiyan, Mehdi ddc 510 misc Cayley graph misc Vertex transitive misc Edge transitive misc Normal edge transitive misc Normal graph misc Automorphism group Non-normal edge-transitive directed Cayley graphs of abelian groups
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topic_title	510 ASE Non-normal edge-transitive directed Cayley graphs of abelian groups Cayley graph (dpeaa)DE-He213 Vertex transitive (dpeaa)DE-He213 Edge transitive (dpeaa)DE-He213 Normal edge transitive (dpeaa)DE-He213 Normal graph (dpeaa)DE-He213 Automorphism group (dpeaa)DE-He213
topic	ddc 510 misc Cayley graph misc Vertex transitive misc Edge transitive misc Normal edge transitive misc Normal graph misc Automorphism group
topic_unstemmed	ddc 510 misc Cayley graph misc Vertex transitive misc Edge transitive misc Normal edge transitive misc Normal graph misc Automorphism group
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title	Non-normal edge-transitive directed Cayley graphs of abelian groups
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title_full	Non-normal edge-transitive directed Cayley graphs of abelian groups
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author_browse	Alaeiyan, Mehdi Mirzajani, Javad
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title_sort	non-normal edge-transitive directed cayley graphs of abelian groups
title_auth	Non-normal edge-transitive directed Cayley graphs of abelian groups
abstract	For a group G, and a subset S of G such that $ 1_{G} $ ∉ S, let X = Cay(G,S) be the corresponding Cayley graph. Then X is said to be normal edge transitive if NAut(X)(G) is transitive on edges. In this paper, we determine all connected directed Cayley graphs of finite abelian groups with valency at most 3 which are normal edge transitive but not normal. AMS 05C10; 05C25
abstractGer	For a group G, and a subset S of G such that $ 1_{G} $ ∉ S, let X = Cay(G,S) be the corresponding Cayley graph. Then X is said to be normal edge transitive if NAut(X)(G) is transitive on edges. In this paper, we determine all connected directed Cayley graphs of finite abelian groups with valency at most 3 which are normal edge transitive but not normal. AMS 05C10; 05C25
abstract_unstemmed	For a group G, and a subset S of G such that $ 1_{G} $ ∉ S, let X = Cay(G,S) be the corresponding Cayley graph. Then X is said to be normal edge transitive if NAut(X)(G) is transitive on edges. In this paper, we determine all connected directed Cayley graphs of finite abelian groups with valency at most 3 which are normal edge transitive but not normal. AMS 05C10; 05C25
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title_short	Non-normal edge-transitive directed Cayley graphs of abelian groups
url	https://dx.doi.org/10.1186/2251-7456-7-7
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up_date	2024-07-03T15:03:20.119Z
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