6度1-正則Cay ley圖

李靖建,徐尚進(jìn),楊旭

(1.云南大學(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院,云南昆明 650031;2.廣西大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院,廣西南寧 530004)

6度1-正則Cay ley圖

李靖建1,2,徐尚進(jìn)2,楊旭2

(1.云南大學(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院,云南昆明 650031;2.廣西大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院,廣西南寧 530004)

試圖對(duì)6度1-正則Cayley圖給一個(gè)完全分類.利用無核的概念將圖自同構(gòu)群歸結(jié)到對(duì)稱群S6的子群.然后根據(jù)1-正則圖的性質(zhì)構(gòu)造出所有可能的具有非交換點(diǎn)穩(wěn)定子群的無核6度1-正則Cayley圖,進(jìn)一步證明了構(gòu)造出的圖都是有核的,由此給出了這一類圖的一個(gè)完全分類.

1-正則;Cayley圖;無核

DO I：10.3969/j.issn.1008-5513.2013.05.005

1 引言

2 預(yù)備知識(shí)

3 定理的證明

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1-regu lar Cay ley graphs o f va len cy 6

Li Jingjian1,2,Xu Shangjin2,Yang Xu2

(1.School of M athem atics and Statistics,Yunnan University,Kunm ing 650031,China;
2.School of M athem atics and In form ation Sciences,Guangxi University,Nanning 530004,China)

This paper is trying to give a com p lete classif cation of 1-regu lar Cayley graphs of valency 6.By the def nition of core-free,this paper reduces the graph automorphism group to a subgroup of symmetric group S6. Furthermore,by the p roperties of 1-regu lar graph,this paper constructs all the 1-regular Cayley graphs w ith nonabelian stabilizers and p roves that every such graph is not core-free.Thus a classif cation of such graphs is given.

1-regu lar,Cay ley graph,core-free

O157

A

1008-5513(2013)05-0472-05

2013-06-22.

國家自然科學(xué)基金(10961004,11226141,11361006);廣西自然科學(xué)基金(2013GXNSFAA 019018,2013GXNSFBA 019018).

李靖建(1976-),博士,講師,研究方向：群與圖.

徐尚進(jìn)(1959-),博士,教授,研究方向：群與圖.

2010 MSC:05C25