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一类3p^2阶4度1-正则图

A Family of 4-Valent One-Regular Graphs of Order 3p^2
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摘要 设p为大于3的素数,群G=<a,b,c|a^p=c^p=b^3=1=[a,c],a^b=c,c^b=a^(-1)c^(-1)>和H=<a,b|a^p^2=b^3=1,a^b=a^r>(其中r(?)1(mod p^2),r^3≡1(mod p^2),3|(p-1))是两类3p^2阶非交换群.通过研究Cayley图的正规性,完成了对G和H的所有4度Cayley图的分类,并得到了一类新的4度1-正则图. Let p be a prime and p 3,G = a,b,c|a^p = c^p = b^3 = 1 =[a,c],a^b = c,c^b = a^(-1)c^(-1)and H = a,b|a^p^2 = b^3 = 1,a^b = a^r(where r =■ 1(mod p^2),r^3 = 1(mod p^2),3|(p-1)) are two non-Abelian goups of order 3p^2.In this paper,we classify all tetravalent Cayley graphs of G and H by investigating the normality of Cayley.As a byproduct,we obtain an infinite family of 4-valent one-regular graphs of order 3p^2.
出处 《数学的实践与认识》 CSCD 北大核心 2010年第22期211-215,共5页 Mathematics in Practice and Theory
基金 国家自然科学基金(No10961004) 河南省教育厅基金(2010A110021)
关键词 CAYLEY图 正规CAYLEY图 1-正则图 〈Keyword〉Cayley graph normal Cayley graph one-regular graph
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参考文献10

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