| 图的笛卡儿积的测地数 |
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| 引用本文： | 叶永升,吕长虹,刘庆敏.图的笛卡儿积的测地数[J].应用数学,2007,20(1):158-163. |
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| 作者姓名： | 叶永升 吕长虹 刘庆敏 |
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| 作者单位： | 1. 淮北煤炭师范学院数学系,安徽,淮北,235000;华东师范大学数学系,上海,200062
2. 华东师范大学数学系,上海,200062 |
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| 基金项目： | 国家自然科学基金;上海市科委资助项目;安徽省自然科学基金 |
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| 摘 要： | 对于图G内的任意两点u和v，u-v测地线是指u和v之间的最短路．I（u，v）表示位于u-v测地线上所有点的集合，对于．S∈V（G），I（S）表示所有I（u，v）的并，这里“u,v∈．S．G的测地数g（G）是使I（S）=V（G）的点集．S的最小基数．在这篇文章，我们研究G×K3的测地数和g（G）与g（G×K3）相等的充分必要条件，还给出了T×Km和Cn×Km的测地数，这里T是树．
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| 关 键 词： | 凸集 笛卡儿积 测地线 测地数 |
| 文章编号： | 1001-9847(2007)01-0158-06 |
| 修稿时间： | 2006-06-19 |
The Geodetic Numbers of Cartesian Products of Graphs |
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| YE Yong-sheng,LV Chang-hong,LIU Qing-min.The Geodetic Numbers of Cartesian Products of Graphs[J].Mathematica Applicata,2007,20(1):158-163. |
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| Authors: | YE Yong-sheng LV Chang-hong LIU Qing-min |
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| Institution: | 1. Department of Mathematics, Huaibei Coal Industry Teachers College, Huaibei 235000, China 2. Department of Mathematics, East China Normal University, Shanghai 200062, China |
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| Abstract: | For any two vertices u and v in a graph G,a u-v geodesic is the shortest path between u and v.Let I(u,v) denote the set of all vertices lying on a u-v geodesic.For a vertex subset S,let I(S) denote the union of all I(u,v) for u,v∈S.The geodetic number g(G) of a graph G is the minimum cardinality of a set S with I(S)=V(G).In this paper,a sufficient and necessary condition for the equality of g(G) and g(G×K3) is presented,and for a tree T,we give the geodetic number of T×Km and Cn×Km. |
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| Keywords: | Convex set Cartesian product Geodesic Geodetic number |
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