Counting peaks on graphs
Counting peaks on graphs
复制标题
计算图表上的峰值
DOI：
10.24049/aq.5.1.2
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Mohamed Omar
中科院分区：
文献类型：
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作者：
Alexander Diaz;Lucas Everham;P. Harris;Erik Insko;Vincent Marcantonio;Mohamed Omar
给定一个有n个顶点的图G，用整数1，2，. . .，n，我们说G在顶点v有一个峰，如果v的次数大于或等于2，并且如果v上的标号大于它所有邻居的标号。固定一组S V（G）。我们想确定G的顶点的不同双射标号的个数，使得S中的顶点正好是G的顶点。集合S称为图G的峰集，所有具有峰集S的标号的集合记为P（S;G）。这个定义是对ISSN：2202-3518中峰组研究的推广。在CC BY 4.0国际许可证A下发布。DIAZ-LOPEZ等人/澳大利亚J. COMBIN. 75（2）（2019），174-189 175排列，因为该工作是G是n个顶点上的路径图的特殊情况。本文给出了对任意S ∈ V（G）构造P（S;G）中所有双射标号的一个算法。我们还使用组合的方法来探索在某些研究良好的家庭图的峰值集。
Given a graph G with n vertices and a bijective labeling of the vertices using the integers 1, 2, . . . , n, we say G has a peak at vertex v if the degree of v is greater than or equal to 2, and if the label on v is larger than the label of all its neighbors. Fix a set S ⊂ V (G). We want to determine the number of distinct bijective labelings of the vertices of G, such that the vertices in S are precisely the peaks of G. The set S is called the peak set of the graph G, and the set of all labelings with peak set S is denoted by P (S;G). This definition generalizes the study of peak sets of ISSN: 2202-3518 c ©The author(s). Released under the CC BY 4.0 International License A. DIAZ-LOPEZ ET AL. /AUSTRALAS. J. COMBIN. 75 (2) (2019), 174–189 175 permutations, as that work is the special case of G being the path graph on n vertices. In this paper, we present an algorithm for constructing all of the bijective labelings in P (S;G) for any S ⊆ V (G). We also use combinatorial methods to explore peak sets in certain well-studied families of graphs.
峰值多项式正性猜想的证明
DOI：
10.1016/j.jcta.2017.01.004
发表时间：
2017
期刊：
Series A
影响因子：
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作者：
Diaz-Lopez, Alexander;Harris, Pamela E.;Insko, Erik;Omar, Mohamed
通讯作者：
Omar, Mohamed