| 围长为r的n阶本原有向图的点指数 |
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| 引用本文： | 王龙芹,檀江华,秦峰,孙苗苗.围长为r的n阶本原有向图的点指数[J].纯粹数学与应用数学,2010,26(4):626-629. |
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| 作者姓名： | 王龙芹 檀江华 秦峰 孙苗苗 |
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| 作者单位： | 滁州学院数学系,安徽,滁州,239012;滁州学院数学系,安徽,滁州,239012;滁州学院数学系,安徽,滁州,239012;滁州学院数学系,安徽,滁州,239012 |
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| 基金项目： | 国家自然科学基金，安徽省高校优秀青年人才基金，滁州学院大学生科研项目 |
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| 摘 要： | 研究本原有向图的顶点指数,运用图论与数论方法,得到了n阶围长为r的本原有向图的点指数expD（k）的上界：若rn,且r为素数,D∈Dn,r={D｜D为n阶本原有向图且围长为r},则expD（n,k）=rn-2r＋k（1≤k≤n）;若r｜n,且r为素数或素数的幂,D∈Dn,r,则expD（n,1）=rn-3r＋2.
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| 关 键 词： | 本原有向图 Frobenius数 点指教 |
The vertex exponent of primitive diagraph of order n with girth r |
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| WANG Long-qin,TAN Jiang-hua,QIN Feng,SUN Miao-maio.The vertex exponent of primitive diagraph of order n with girth r[J].Pure and Applied Mathematics,2010,26(4):626-629. |
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| Authors: | WANG Long-qin TAN Jiang-hua QIN Feng SUN Miao-maio |
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| Institution: | WANG Long-qin,TAN Jiang-hua,QIN Feng,SUN Miao-maio(Department of Mathematics,Chuzhou University,Chuzhou,Anhui 239012,China) |
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| Abstract: | This paper discusses the vertex exponent for the class of primitive diagraph.By using graph theoretical methods and combinatorial method,it proves that the maximum value of vertex exponent of primitive diagraph of order n with girth r is as follows：if r n,r is a prime number,and D is a primitive diagraph of order n with girth r,then expD（n,k） = rn-2r ＋ k（1 ≤ k ≤ n）;if r ｜ n,r is a prime number or its positive power,and D is a primitive diagraph of order n with girth r,then expD（n,1） = rn-3r ＋ 2. |
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| Keywords: | primitive diagraph Frobenius number vertex exponent |
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