Discrete Applied Mathematics最新文献

英文中文

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2024-08-31 DOI: 10.1016/j.dam.2024.08.016

Robert Scheffler

We present a new subclass of interval graphs that generalizes connected proper interval graphs. These graphs are characterized by vertex orderings called connected perfect elimination orderings (PEO), i.e., PEOs where consecutive vertices are adjacent. Alternatively, these graphs can also be characterized by special interval models and clique orderings. We present a linear-time recognition algorithm that uses PQ-trees. Furthermore, we study the behavior of multi-sweep graph searches on this graph class. This study also shows that Corneil’s well-known LBFS-recognition algorithm for proper interval graphs can be generalized to a large family of graph searches. Finally, we show that a strong result on the existence of Hamiltonian paths and cycles in proper interval graphs can be generalized to semi-proper interval graphs.

我们提出了一种新的区间图子类，它概括了连通的适当区间图。这些图的顶点排序称为连通完全消元排序（PEO），即连续顶点相邻的 PEO。或者，这些图也可以用特殊的区间模型和簇排序来表征。我们提出了一种使用 PQ 树的线性时间识别算法。此外，我们还研究了多扫图搜索在这类图上的行为。这项研究还表明，Corneil 著名的适当区间图 LBFS 识别算法可以推广到一大类图搜索。最后，我们还证明了在适当区间图中存在哈密尔顿路径和循环的强大结果可以推广到半适当区间图。

引用次数: 0

Shapley–Folkman-type theorem for integrally convex sets 积分凸集的 Shapley-Folkman 型定理

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2024-08-31 DOI: 10.1016/j.dam.2024.08.015

Kazuo Murota , Akihisa Tamura

The Shapley–Folkman theorem is a statement about the Minkowski sum of (non-convex) sets, expressing the closeness of the Minkowski sum to convexity in a quantitative manner. This paper establishes similar theorems for integrally convex sets, M $^{♮}$ -convex sets, and L $^{♮}$ -convex sets, which are major classes of discrete convex sets in discrete convex analysis.

沙普利-福克曼定理是关于（非凸）集合的闵科夫斯基和的一个陈述，以定量的方式表达了闵科夫斯基和与凸性的接近程度。本文为积分凸集、M♮凸集和 L♮凸集建立了类似的定理，它们是离散凸分析中离散凸集的主要类别。

引用次数: 0

On locally finite ordered rooted trees and their rooted subtrees 关于局部有限有序有根树及其有根子树

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2024-08-31 DOI: 10.1016/j.dam.2024.08.014

Geir Agnarsson , Elie Alhajjar , Aleyah Dawkins

<div>We first revisit and generalize a known result about a doubly exponential sequence that describes the number of <math><mi>k</mi></math>-ary ordered rooted trees of height <math><mi>h</mi></math> where <math><mrow><mi>k</mi><mo>≥</mo><mn>2</mn></mrow></math> is a fixed integer. Such a sequence has the form <math><msub><mrow><mrow><mo>(</mo><msub><mrow><mi>t</mi></mrow><mrow><mi>k</mi></mrow></msub><mrow><mo>(</mo><mi>h</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow><mrow><mi>h</mi><mo>≥</mo><mn>0</mn></mrow></msub></math> where <math><mrow><msub><mrow><mi>t</mi></mrow><mrow><mi>k</mi></mrow></msub><mrow><mo>(</mo><mi>h</mi><mo>)</mo></mrow><mo>=</mo><mfenced><mrow><mi>c</mi><msup><mrow><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow><mrow><msup><mrow><mi>k</mi></mrow><mrow><mi>h</mi></mrow></msup></mrow></msup></mrow></mfenced><mo>−</mo><mn>1</mn></mrow></math> for each given <math><mi>k</mi></math> and <math><mrow><mi>c</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mo>∈</mo></mrow></math><math><mi>R</mi></math>. We provide the first detailed analysis of the real number sequence <math><msub><mrow><mrow><mo>(</mo><mi>c</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow><mrow><mi>k</mi><mo>≥</mo><mn>2</mn></mrow></msub></math> and show, in particular, that this sequence is strictly decreasing and has a limit 2 when <math><mi>k</mi></math> tends to infinity. We then turn our attention to a more general setting for sequences that describe the number of ordered rooted trees of a given height. This has applications in algorithm analyses where searches in rooted trees are performed. We consider infinite ordered rooted trees in which each ordered rooted subtree induced by all the vertices on levels <math><mrow><mi>h</mi><mo>∈</mo></mrow></math><math><mi>N</mi></math>or less is a finite ordered rooted tree of height <math><mi>h</mi></math> of a certain type. In particular, we study those infinite trees <math><mi>T</mi></math> in which each vertex has infinitely many descendants. We first give a complete characterization of those infinite trees for which the number <math><mrow><mi>s</mi><mrow><mo>(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>h</mi></mrow></msub><mo>)</mo></mrow></mrow></math> of ordered rooted subtrees <math><msub><mrow><mi>T</mi></mrow><mrow><mi>n</mi></mrow></msub></math> of height at most <math><mi>h</mi></math> of <math><mi>T</mi></math> is bounded by a polynomial in <math><mi>h</mi></math>. We then present natural lower and upper bounds for <math><mrow><mi>s</mi><mrow><mo>(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>h</mi></mrow></msub><mo>)</mo></mrow></mrow></math> and use those to obtain a tight threshold function <math><mrow><mi>f</mi><mrow

我们首先重温并推广一个已知结果，即描述高度为 h 的 k 有序有根树的双指数序列，其中 k≥2 是一个固定整数。这样一个序列的形式是 (tk(h))h≥0 其中对于每个给定的 k 和 c(k)∈R，tk(h)=c(k)kh-1。我们首次详细分析了实数序列 (c(k))k≥2，并特别指出，当 k 趋于无穷大时，该序列严格递减并具有极限 2。然后，我们将注意力转向描述给定高度的有序有根树数量的序列的更一般设置。这适用于在有根树上进行搜索的算法分析。我们考虑的是无限有序有根树，在这些有序有根树中，高度 h∈Nor 小于 h 的所有顶点所诱导的每棵有序有根子树都是高度为 h 的某一类型的有限有序有根树。我们尤其要研究那些每个顶点都有无限多后代的无限树 T。我们首先给出了这些无限树的完整特征，对于这些树，T 的高度不超过 h 的有序有根子树 Tn 的数量 s(Th) 是以 h 的多项式为界的。然后，我们给出了 s(Th) 的自然下界和上界，并利用这些下界和上界得到了一个严密的阈值函数 f(h)，对于这个函数，我们有 s(Th)=Θ(hf(h)) 来表示无限多的 h∈N。这个阈值函数可以用兰伯特 W 函数来表示，即函数 w↦wew 的两个反函数的上分支。最后，我们研究了 s(Th)的一些理论性质，这些性质适用于将树根视为唯一最大元素的部分有序集合（posets）时具有有限宽度的无限树 T。我们特别指出，对于足够大的 h，函数 s(Th) 是由 h 的多项式给出的，并且我们确定了这个多项式的阶数和前导系数。

引用次数: 0

Eccentricity matrix of corona of two graphs 两图日冕的偏心矩阵

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2024-08-29 DOI: 10.1016/j.dam.2024.08.017

Smrati Pandey, Lavanya Selvaganesh, Jesmina Pervin

The eccentricity matrix, $ɛ (G)$ , of a graph $G$ is derived from the distance matrix by letting the $u v$ -th element to be equal to the distance between two vertices $u$ and $v$ , if the distance is the minimum of their eccentricities and zero otherwise. In this article, we study the spectrum of $ɛ (G)$ and establish an upper bound for its $ɛ$ -spectral radius when $G$ is a self-centered graph.

Further, we explore the structure of $ɛ (G \circ H)$ , where $G \circ H$ is the corona product of a self-centered graph $G$ and a graph $H$ . We characterize the irreducibility of $ɛ (G \circ H)$ and, in this process, find that it is independent of $ɛ (H)$ , which allows us to construct infinitely many graphs with irreducible eccentricity matrix. Moreover, we compute the complete spectrum of $ɛ (G \circ H)$ including its $ɛ$ -eigenvectors, $ɛ$ -energy, and $ɛ$ -inertia. Finally, we conclude that several non-isomorphic $ɛ$ -co-spectral graphs can be generated using the corona product of two graphs.

图 G 的偏心矩阵ɛ(G)由距离矩阵导出，如果两个顶点 u 和 v 之间的距离是它们偏心率的最小值，则 uv 元素等于这两个顶点之间的距离，否则为零。在本文中，我们研究了ɛ(G)的谱，并建立了当 G 是自中心图时其ɛ谱半径的上限。此外，我们还探索了ɛ(G∘H)的结构，其中 G∘H 是自中心图 G 和图 H 的日冕积。我们描述了ɛ(G∘H)的不可还原性，并在此过程中发现它与ɛ(H)无关，这使得我们可以构造无限多具有不可还原偏心矩阵的图。此外，我们还计算了ɛ(G∘H)的完整谱，包括它的ɛ特征向量、ɛ能量和ɛ惯性。最后，我们得出结论：利用两个图形的日冕积，可以生成多个非同构的ɛ-共谱图。

{"title":"Eccentricity matrix of corona of two graphs","authors":"Smrati Pandey, Lavanya Selvaganesh, Jesmina Pervin","doi":"10.1016/j.dam.2024.08.017","DOIUrl":"10.1016/j.dam.2024.08.017","url":null,"abstract":"<div>The eccentricity matrix, <math><mrow><mi>ɛ</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math>, of a graph <math><mi>G</mi></math> is derived from the distance matrix by letting the <math><mrow><mi>u</mi><mi>v</mi></mrow></math>-th element to be equal to the distance between two vertices <math><mi>u</mi></math> and <math><mi>v</mi></math>, if the distance is the minimum of their eccentricities and zero otherwise. In this article, we study the spectrum of <math><mrow><mi>ɛ</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math> and establish an upper bound for its <math><mi>ɛ</mi></math>-spectral radius when <math><mi>G</mi></math> is a self-centered graph.Further, we explore the structure of <math><mrow><mi>ɛ</mi><mrow><mo>(</mo><mi>G</mi><mo>∘</mo><mi>H</mi><mo>)</mo></mrow></mrow></math>, where <math><mrow><mi>G</mi><mo>∘</mo><mi>H</mi></mrow></math> is the corona product of a self-centered graph <math><mi>G</mi></math> and a graph <math><mi>H</mi></math>. We characterize the irreducibility of <math><mrow><mi>ɛ</mi><mrow><mo>(</mo><mi>G</mi><mo>∘</mo><mi>H</mi><mo>)</mo></mrow></mrow></math> and, in this process, find that it is independent of <math><mrow><mi>ɛ</mi><mrow><mo>(</mo><mi>H</mi><mo>)</mo></mrow></mrow></math>, which allows us to construct infinitely many graphs with irreducible eccentricity matrix. Moreover, we compute the complete spectrum of <math><mrow><mi>ɛ</mi><mrow><mo>(</mo><mi>G</mi><mo>∘</mo><mi>H</mi><mo>)</mo></mrow></mrow></math> including its <math><mi>ɛ</mi></math>-eigenvectors, <math><mi>ɛ</mi></math>-energy, and <math><mi>ɛ</mi></math>-inertia. Finally, we conclude that several non-isomorphic <math><mi>ɛ</mi></math>-co-spectral graphs can be generated using the corona product of two graphs.</div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"359 ","pages":"Pages 354-363"},"PeriodicalIF":1.0,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142097916","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Total-rainbow connection and forbidden subgraphs 全彩虹连接和禁止子图

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2024-08-29 DOI: 10.1016/j.dam.2024.07.051

Jingshu Zhang , Hui Jiang , Wenjing Li

A path in a total-colored graph $G$ is called a total-rainbow path if its edges and internal vertices have distinct colors. The total-colored graph $G$ is total-rainbow connected if for any two distinct vertices of $G$ , there is a total-rainbow path connecting them. The total-rainbow connection number of $G$ , denoted as $t r c (G)$ , represents the minimum number of colors that are required to make $G$ total-rainbow connected. This paper characterizes all the families $F$ of connected graphs with $| F | \in {1, 2}$ , for which there exists a constant $k_{F}$ such that $G$ being a connected $F$ -free graph implies $t r c (G) \leq 2 d i a m (G) + k_{F}$ , where $d i a m (G)$ denotes the diameter of $G$ .

如果全彩色图 G 中的边和内部顶点都有不同的颜色，则该图中的路径称为全彩虹路径。如果对于 G 中任意两个不同的顶点，存在一条连接它们的全彩虹路径，那么全彩色图 G 就是全彩虹连接图。G 的全彩虹连接数表示使 G 全彩虹连接所需的最少颜色数，用 trc(G) 表示。本文描述了|F|∈{1,2}的所有连通图族 F，对于这些族 F，存在一个常数 kF，使得 G 作为无 F 连通图意味着 trc(G)≤2diam(G)+kF，其中 diam(G) 表示 G 的直径。

引用次数: 0

Graphs with degree sequence {(m−1)m,(n−1)n} and {mn,nm} 阶数序列为 {(m-1)m,(n-1)n} 和 {mn,nm} 的图形

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2024-08-26 DOI: 10.1016/j.dam.2024.08.009

Boris Brimkov , Valentin Brimkov

In this paper we study the class of graphs $G_{m, n}$ that have the same degree sequence as two disjoint cliques $K_{m}$ and $K_{n}$ , as well as the class ${\bar{G}}_{m, n}$ of the complements of such graphs. We establish various properties of $G_{m, n}$ and ${\bar{G}}_{m, n}$ related to recognition, connectivity, diameter, bipartiteness, Hamiltonicity, and pancyclicity. We also show that several classical optimization problems on these graphs are NP-hard, while others can be solved efficiently.

在本文中，我们研究了与两个不相交的小群 Km 和 Kn 具有相同度序列的一类图 Gm,n，以及这类图的补集 G¯m,n。我们建立了 Gm,n 和 G¯m,n 的与识别、连通性、直径、两部分性、汉密尔顿性和泛周期性有关的各种性质。我们还证明了这些图上的几个经典优化问题是 NP-困难的，而其他问题则可以高效求解。

引用次数: 0

Squares of graphs are optimally (s,t)-supereulerian 图形的正方形是最优的（s,t）上位图

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2024-08-24 DOI: 10.1016/j.dam.2024.08.013

Yue Yan , Lan Lei , Yang Wu , Hong-Jian Lai

<div>For two integers <math><mrow><mi>s</mi><mo>≥</mo><mn>0</mn><mo>,</mo><mi>t</mi><mo>≥</mo><mn>0</mn></mrow></math>, a graph <math><mi>G</mi></math> is <math><mrow><mo>(</mo><mi>s</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow></math>-supereulerian, if for every pair of disjoint subsets <math><mrow><mi>X</mi><mo>,</mo><mi>Y</mi><mo>⊂</mo><mi>E</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math>, with <math><mrow><mrow><mo>|</mo><mi>X</mi><mo>|</mo></mrow><mo>≤</mo><mi>s</mi><mo>,</mo><mrow><mo>|</mo><mi>Y</mi><mo>|</mo></mrow><mo>≤</mo><mi>t</mi></mrow></math>, <math><mi>G</mi></math> has a spanning eulerian subgraph <math><mi>H</mi></math> with <math><mrow><mi>X</mi><mo>⊂</mo><mi>E</mi><mrow><mo>(</mo><mi>H</mi><mo>)</mo></mrow></mrow></math> and <math><mrow><mi>Y</mi><mo>∩</mo><mi>E</mi><mrow><mo>(</mo><mi>H</mi><mo>)</mo></mrow><mo>=</mo><mo>0̸</mo></mrow></math>. Pulleyblank (1979) proved that even within planar graphs, determining if a graph <math><mi>G</mi></math> is <math><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></math>-supereulerian is NP-complete. Xiong et al. (2021) identified a function <math><mrow><msub><mrow><mi>j</mi></mrow><mrow><mn>0</mn></mrow></msub><mrow><mo>(</mo><mi>s</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow></mrow></math> such that every <math><mrow><mo>(</mo><mi>s</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow></math>-supereulerian graph must have edge connectivity at least <math><mrow><msub><mrow><mi>j</mi></mrow><mrow><mn>0</mn></mrow></msub><mrow><mo>(</mo><mi>s</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow></mrow></math>. Examples have been found that having edge connectivity at least <math><mrow><msub><mrow><mi>j</mi></mrow><mrow><mn>0</mn></mrow></msub><mrow><mo>(</mo><mi>s</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow></mrow></math> is not sufficient to warrant the graph to be <math><mrow><mo>(</mo><mi>s</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow></math>-supereulerian. A graph family <math><mrow><mi>S</mi></mrow></math> is optimally <math><mrow><mo>(</mo><mi>s</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow></math>-supereulerian if for every pair of given non-negative integers <math><mrow><mo>(</mo><mi>s</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow></math>, a graph <math><mrow><mi>G</mi><mo>∈</mo><mi>S</mi></mrow></math> is <math><mrow><mo>(</mo><mi>s</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow></math>-supereulerian if and only if <math><mrow><msup><mrow><mi>κ</mi></mrow><mrow><mo>′</mo></mrow></msup><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>≥</mo><msub><mrow><mi>j</mi></mrow><mrow><mn>0</mn></mrow></msub><mrow><mo>(</mo><mi>s</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow></mrow></math>

对于两个整数 s≥0,t≥0，如果对于每一对不相交的子集 X,Y⊂E(G)，且 |X|≤s,|Y|≤t，G 有一个跨优勒子图 H，且 X⊂E(H)和 Y∩E(H)=0̸, 则图 G 是 (s,t)-supereulerian 的。Pulleyblank (1979) 证明，即使在平面图中，确定一个图 G 是否为 (0,0)-supereulerian 也是 NP-完全的。Xiong 等人（2021 年）发现了一个函数 j0(s,t)，使得每个 (s,t)-supereulerian 图必须至少具有 j0(s,t) 的边连接性。实例表明，边缘连通性至少为 j0(s,t)并不足以保证图是（s,t）-超等图。如果对于每一对给定的非负整数 (s,t)，当且仅当κ′(G)≥j0(s,t)时，图 G∈S 是 (s,t)-supereulerian 的，则图族 S 是最优 (s,t)-supereulerian 的。因此，在这样的图族中，(s,t)-上ereulerian 问题可在多项式时间内求解，且对边连接性的要求极低。在本研究中，我们证明了阶数至少为 5 的所有正方形图族是最优 (s,t)-supereulerian 的。

引用次数: 0

On k-shifted antimagic spider forests 关于 k 移位的反魔法蜘蛛森林

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2024-08-24 DOI: 10.1016/j.dam.2024.07.036

Fei-Huang Chang , Wei-Tian Li , Daphne Der-Fen Liu , Zhishi Pan

Let $G (V, E)$ be a simple graph with $m$ edges. For a given integer $k$ , a $k$ -shifted antimagic labeling is a bijection $f : E (G) \to {k + 1, k + 2, \dots, k + m}$ such that all vertices have different vertex-sums, where the vertex-sum of a vertex $v$ is the sum of the labels assigned to the edges incident to $v$ . A graph $G$ is $k$ -shifted antimagic if it admits a $k$ -shifted antimagic labeling. For the special case when $k = 0$ , a 0-shifted antimagic labeling is known as antimagic labeling; and $G$ is antimagic if it admits an antimagic labeling. A spider is a tree with exactly one vertex of degree greater than two. A spider forest is a graph where each component is a spider. In this article, we prove that certain spider forests are $k$ -shifted antimagic for all $k ⩾ 0$ . In addition, we show that for a spider forest $G$ with $m$ edges, there exists a positive integer $k_{0} < m$ such that $G$ is $k$ -shifted antimagic for all $k ⩾ k_{0}$ and $k ⩽ - (m + k_{0} + 1)$ .

假设 G(V,E) 是一个有 m 条边的简单图。对于给定的整数 k，k 移位反魔法标签是一个双射 f:E(G)→{k+1,k+2,...,k+m}，使得所有顶点具有不同的顶点和，其中顶点 v 的顶点和是分配给 v 所带边的标签之和。在 k=0 的特殊情况下，0 移位反魔法标签被称为反魔法标签；如果图 G 允许反魔法标签，那么它就是反魔法图。蜘蛛图是指一个顶点的阶数大于 2 的树。蜘蛛森林是每个组成部分都是蜘蛛的图。在本文中，我们证明了某些蜘蛛森林在所有 k⩾0 条件下都是 k 移位反魔法的。此外，我们还证明，对于有 m 条边的蜘蛛森林 G，存在一个正整数 k0<m，使得 G 在所有 k⩾k0 和 k⩽-(m+k0+1) 条件下都是 k 移位反魔术的。

{"title":"On k-shifted antimagic spider forests","authors":"Fei-Huang Chang , Wei-Tian Li , Daphne Der-Fen Liu , Zhishi Pan","doi":"10.1016/j.dam.2024.07.036","DOIUrl":"10.1016/j.dam.2024.07.036","url":null,"abstract":"<div>Let <math><mrow><mi>G</mi><mrow><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></mrow></mrow></math> be a simple graph with <math><mi>m</mi></math> edges. For a given integer <math><mi>k</mi></math>, a <math><mi>k</mi></math>-shifted antimagic labeling is a bijection <math><mrow><mi>f</mi><mo>:</mo><mi>E</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>→</mo><mrow><mo>{</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>k</mi><mo>+</mo><mn>2</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>k</mi><mo>+</mo><mi>m</mi><mo>}</mo></mrow></mrow></math> such that all vertices have different vertex-sums, where the vertex-sum of a vertex <math><mi>v</mi></math> is the sum of the labels assigned to the edges incident to <math><mi>v</mi></math>. A graph <math><mi>G</mi></math> is <math><mi>k</mi></math>-shifted antimagic if it admits a <math><mi>k</mi></math>-shifted antimagic labeling. For the special case when <math><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow></math>, a 0-shifted antimagic labeling is known as antimagic labeling; and <math><mi>G</mi></math> is antimagic if it admits an antimagic labeling. A spider is a tree with exactly one vertex of degree greater than two. A spider forest is a graph where each component is a spider. In this article, we prove that certain spider forests are <math><mi>k</mi></math>-shifted antimagic for all <math><mrow><mi>k</mi><mo>⩾</mo><mn>0</mn></mrow></math>. In addition, we show that for a spider forest <math><mi>G</mi></math> with <math><mi>m</mi></math> edges, there exists a positive integer <math><mrow><msub><mrow><mi>k</mi></mrow><mrow><mn>0</mn></mrow></msub><mo><</mo><mi>m</mi></mrow></math> such that <math><mi>G</mi></math> is <math><mi>k</mi></math>-shifted antimagic for all <math><mrow><mi>k</mi><mo>⩾</mo><msub><mrow><mi>k</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></math> and <math><mrow><mi>k</mi><mo>⩽</mo><mo>−</mo><mrow><mo>(</mo><mi>m</mi><mo>+</mo><msub><mrow><mi>k</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mrow></math>.</div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"358 ","pages":"Pages 468-476"},"PeriodicalIF":1.0,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0166218X24003391/pdfft?md5=2002cef3181394859c5f2db48d9e05e5&pid=1-s2.0-S0166218X24003391-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142049338","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The zero forcing number of claw-free cubic graphs 无爪立方图的零强制数

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2024-08-24 DOI: 10.1016/j.dam.2024.08.011

Mengya He , Huixian Li , Ning Song , Shengjin Ji

Let $G$ be a simple graph of order $n$ . Let $S$ be a coloring subset of $V (G)$ . The forcing process is that a colored vertex forces the uncolored neighbor to be colored if it has exactly one uncolored neighbor. The set $S$ is a zero forcing set if all vertices of $G$ become colored by iteratively applying the forcing process. The minimum size of a zero forcing set in a graph $G$ is zero forcing number, denoted by $Z (G)$ , which is proposed in 2008 as a natural upper bound of the maximum nullity regarding the graph $G$ . In the paper, we bound the zero forcing number in connected claw-free cubic graphs. More exactly if $G (\neq K_{4})$ is a connected claw-free cubic graph with order $n$ , then we prove that $Z (G) \leq α (G)$ except for three graphs with small order, and then $Z (G) \leq \frac{n}{4} + 1$ except for three classes of graphs. In fact, our results give affirmative answers for two open problems raised by Davila and Henning.

设 G 是阶数为 n 的简单图，S 是 V(G) 的着色子集。着色过程是，如果一个着色顶点正好有一个未着色的邻居，则该顶点会迫使未着色的邻居着色。如果通过迭代应用强制过程，G 的所有顶点都变成了彩色，那么集合 S 就是零强制集合。图 G 中零强制集的最小大小为零强制数，用 Z(G) 表示，它是 2008 年提出的关于图 G 的最大无效性的自然上限。更确切地说，如果 G(≠K4) 是阶数为 n 的连通无爪立方图，那么我们证明 Z(G)≤α(G) 除了三个阶数较小的图，然后 Z(G)≤n4+1 除了三类图。事实上，我们的结果给出了达维拉和亨宁提出的两个未决问题的肯定答案。

{"title":"The zero forcing number of claw-free cubic graphs","authors":"Mengya He , Huixian Li , Ning Song , Shengjin Ji","doi":"10.1016/j.dam.2024.08.011","DOIUrl":"10.1016/j.dam.2024.08.011","url":null,"abstract":"<div>Let <math><mi>G</mi></math> be a simple graph of order <math><mi>n</mi></math>. Let <math><mi>S</mi></math> be a coloring subset of <math><mrow><mi>V</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math>. The forcing process is that a colored vertex forces the uncolored neighbor to be colored if it has exactly one uncolored neighbor. The set <math><mi>S</mi></math> is a zero forcing set if all vertices of <math><mi>G</mi></math> become colored by iteratively applying the forcing process. The minimum size of a zero forcing set in a graph <math><mi>G</mi></math> is zero forcing number, denoted by <math><mrow><mi>Z</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math>, which is proposed in 2008 as a natural upper bound of the maximum nullity regarding the graph <math><mi>G</mi></math>. In the paper, we bound the zero forcing number in connected claw-free cubic graphs. More exactly if <math><mrow><mi>G</mi><mrow><mo>(</mo><mo>≠</mo><msub><mrow><mi>K</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>)</mo></mrow></mrow></math> is a connected claw-free cubic graph with order <math><mi>n</mi></math>, then we prove that <math><mrow><mi>Z</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>≤</mo><mi>α</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math> except for three graphs with small order, and then <math><mrow><mi>Z</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>≤</mo><mfrac><mrow><mi>n</mi></mrow><mrow><mn>4</mn></mrow></mfrac><mo>+</mo><mn>1</mn></mrow></math> except for three classes of graphs. In fact, our results give affirmative answers for two open problems raised by Davila and Henning.</div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"359 ","pages":"Pages 321-330"},"PeriodicalIF":1.0,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142049995","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On a family of universal cycles for multi-dimensional permutations 论多维排列的通用循环族

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2024-08-24 DOI: 10.1016/j.dam.2024.08.010

Sergey Kitaev , Dun Qiu

A universal cycle (u-cycle) for permutations of length $n$ is a cyclic word, any size $n$ window of which is order-isomorphic to exactly one permutation of length $n$ , and all permutations of length $n$ are covered. It is known that u-cycles for permutations exist, and they have been considered in the literature in several papers from different points of view.

In this paper, we show how to construct a family of u-cycles for multi-dimensional permutations, which is based on applying an appropriate greedy algorithm. Our construction is a generalization of the greedy way by Gao et al. to construct u-cycles for permutations. We also note the existence of u-cycles for $d$ -dimensional matrices.

长度为 n 的排列的普遍循环（u-循环）是一个循环词，其任何大小为 n 的窗口与一个长度为 n 的排列恰好是阶同构的，并且覆盖了所有长度为 n 的排列。众所周知，排列的 u 循环是存在的，文献中已有多篇论文从不同角度对其进行了研究。在本文中，我们展示了如何通过应用适当的贪婪算法来构建多维排列的 u 循环族。我们的构造是对高等人构造u循环的贪婪算法的推广。我们还注意到 d 维矩阵 u 循环的存在。

引用次数: 0

首页上一页

下一页尾页

类型

全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

数据库

全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

Discrete Applied Mathematics

全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.

﹀