| 直径图为11圈的7距离集研究 |
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| 引用本文： | 王 琦,丛 悦,高飞星.直径图为11圈的7距离集研究[J].河北科技大学学报,2016,37(2):146-153. |
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| 作者姓名： | 王 琦 丛 悦 高飞星 |
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| 作者单位： | ;1.河北科技大学理学院 |
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| 基金项目： | 河北省自然科学基金（A2014208095） |
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| 摘 要： | 如果平面点集X中的任意两点确定的互异距离数为k,则称X为k距离集。用d(x,y)表示平面上互异两点x,y之间的距离,记X中的最大距离为直径D=D(X)。直径图DG(XD)是由X中所有直径构成的图,XD表示其顶点集。讨论了当X是一个7距离集时,直径图DG(XD)的构型。利用DG(XD)中最多包含一个圈,且只能为奇圈的特性,以及直径所具有的特殊性,证得当直径图为11圈时,其顶点集XD恰好为某正十一边形的顶点集。
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| 关 键 词： | 离散几何 互异距离 直径图 奇圈 7距离集 |
| 收稿时间： | 2015/10/17 0:00:00 |
| 修稿时间： | 2015/12/15 0:00:00 |
Research on 7-distance set with DG(XD)=C11 |
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| WANG Qi,CONG Yue and GAO Feixing.Research on 7-distance set with DG(XD)=C11[J].Journal of Hebei University of Science and Technology,2016,37(2):146-153. |
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| Authors: | WANG Qi CONG Yue and GAO Feixing |
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| Abstract: | A planar point set X is called a k-distance set if there are exactly k distances between two distinct points in X. Let d(x,y) be the distance of any two distinct points x,y. Let diameter D=D(X) be the longest distance of X. The diameter graph DG(XD) is composed of all diameters in X, where XD is the set of its endpoints. In this paper, the configuration of the diameter graph DG(XD) is discussed when X is a 7-distantce set. It is proved that the endpoint set XD is the endpoint set of the regular 11-sided polygon when the diameter graph has 11 cycles based on the characteristics of DG(XD) containing at most one and only odd cycle and the diameter specialty. |
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| Keywords: | discrete geometry distinct distance diameter graph odd cycle 7-distance set |
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