The edge metric dimensions of convex polytopes

IF 1 3区 数学 Q3 MATHEMATICS, APPLIED
Meiqin Wei , Bohua Fan , Changhong Lu , Jun Yue , Jinfeng Liu
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引用次数: 0

Abstract

Let G=(V,E) be a connected graph. A vertex xV distinguishes the edge pair e1,e2E if the distances from x to e1 and e2 are distinct. A vertex subset SV is an edge metric generator of G if any pair of edges in E can be distinguished by some element of S. The minimum size of an edge metric generator of G is called the edge metric dimension of G and denoted by edim(G). In this paper, we determine the exact values of the edge metric dimensions for some convex polytopes and generalized convex polytopes, which further emphasize the fact that there are families of convex polytopes having greater edge metric dimensions than their metric dimensions. The proof methods in this paper are constructive and they can be implemented through algorithms.
凸多面体的边缘度量尺寸
设G=(V,E)为连通图。如果顶点x∈V与边缘对e1,e2∈E之间的距离不同,则顶点x∈V与边缘对e1,e2∈E之间的距离不同。如果E中的任意一对边可以被S的某个元素区分,则顶点子集S是G的一个边度生成器。G的边度生成器的最小尺寸称为G的边度维数,记为edim(G)。本文确定了一些凸多面体和广义凸多面体的边缘度量维数的精确值,进一步强调了凸多面体族的边缘度量维数大于其度量维数的事实。本文的证明方法具有建设性,可以通过算法实现。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Discrete Applied Mathematics
Discrete Applied Mathematics 数学-应用数学
CiteScore
2.30
自引率
9.10%
发文量
422
审稿时长
4.5 months
期刊介绍: The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal. Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.
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