Discrete Applied Mathematics最新文献

{"title":"An approximate dynamic programming approach for multi-stage stochastic lot-sizing under a Decision–Hazard–Decision information structure","authors":"Victor Spitzer ,&nbsp;Céline Gicquel ,&nbsp;Evgeny Gurevsky ,&nbsp;François Sanson","doi":"10.1016/j.dam.2025.08.051","DOIUrl":"10.1016/j.dam.2025.08.051","url":null,"abstract":"<div><div>This work studies a combinatorial optimization problem encountered in industrial production planning: the single-item multi-resource lot-sizing problem with inventory bounds and lost sales. The demand to be satisfied by the production plan is subject to uncertainty and only probabilistically known. We consider a multi-stage decision process with a Decision–Hazard–Decision information structure in which decisions are made at each stage both before and after the uncertainty is revealed. Such a setting has not yet been studied for stochastic lot-sizing problems, and the resulting problem is modeled as a multi-stage stochastic integer program. We propose a solution approach based on an approximate stochastic dynamic programming algorithm. It relies on a decomposition of the problem into single-stage sub-problems and on the estimation at each stage of the expected future costs. Due to the Decision–Hazard–Decision information structure, each nested single-stage sub-problem is itself a two-stage stochastic integer program. We therefore introduce a Benders decomposition scheme to reduce the computational effort required to solve each nested sub-problem, and present a special-purpose polynomial-time algorithm to efficiently solve the single-scenario second-stage sub-problems involved in the Benders decomposition. The results of extensive simulation experiments carried out on large-size randomly generated instances are reported. They demonstrate the practical benefit, in terms of the actual production cost, of using the proposed approach as compared to a naive deterministic optimization approach based on the expected demand.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"379 ","pages":"Pages 355-378"},"PeriodicalIF":1.0,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145049050","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}

{"title":"Maximal polyomino chains with respect to the Kirchhoff index","authors":"Wensheng Sun ,&nbsp;Yujun Yang ,&nbsp;Shou-Jun Xu","doi":"10.1016/j.dam.2025.08.060","DOIUrl":"10.1016/j.dam.2025.08.060","url":null,"abstract":"<div><div>Let <span><math><mi>G</mi></math></span> be a connected graph. The resistance distance between two vertices <span><math><mi>u</mi></math></span> and <span><math><mi>v</mi></math></span> of <span><math><mi>G</mi></math></span> is defined as the potential difference generated between <span><math><mi>u</mi></math></span> and <span><math><mi>v</mi></math></span> induced by the unique <span><math><mrow><mi>u</mi><mo>→</mo><mi>v</mi></mrow></math></span> flow when a unit current flows in from node <span><math><mi>u</mi></math></span> and flows out from node <span><math><mi>v</mi></math></span>. The Kirchhoff index of <span><math><mi>G</mi></math></span> is defined as the sum of all the resistance distances pairs of <span><math><mi>G</mi></math></span>. Polyomino chains, as an important geometric structure, have been widely studied in statistical physics and mathematical chemistry. In this paper, by employing standard techniques from electrical networks and using comparison results on the Kirchhoff index of <span><math><mrow><mi>S</mi><mo>,</mo><mi>T</mi></mrow></math></span>-isomers, we first show that among all polyomino chains with <span><math><mi>n</mi></math></span> squares, the maximum Kirchhoff index is attained only when the polyomino chain is a “bend-free” chain. Furthermore, according to the recursion formula for the resistance distances, “bend-free” chains with maximum and minimum Kirchhoff index are characterized. As a result, the polyomino chains with maximum Kirchhoff index are obtained.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"380 ","pages":"Pages 34-50"},"PeriodicalIF":1.0,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050666","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}

{"title":"Claw-free cubic graphs are (1, 1, 1, 3)-packing edge-colorable","authors":"Jingxi Hou ,&nbsp;Tao Wang ,&nbsp;Xiaojing Yang","doi":"10.1016/j.dam.2025.08.062","DOIUrl":"10.1016/j.dam.2025.08.062","url":null,"abstract":"<div><div>For a non-decreasing positive integer sequence <span><math><mrow><mi>S</mi><mo>=</mo><mrow><mo>(</mo><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>s</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>)</mo></mrow></mrow></math></span>, an <span><math><mi>S</mi></math></span>-packing edge-coloring of a graph <span><math><mi>G</mi></math></span> is a partition of the edge set of <span><math><mi>G</mi></math></span> into subsets <span><math><mrow><msub><mrow><mi>E</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>k</mi></mrow></msub></mrow></math></span> such that for each <span><math><mrow><mn>1</mn><mo>≤</mo><mi>i</mi><mo>≤</mo><mi>k</mi></mrow></math></span>, the distance between any two distinct edges <span><math><mrow><msub><mrow><mi>e</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>e</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>∈</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></math></span> is at least <span><math><mrow><msub><mrow><mi>s</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>+</mo><mn>1</mn></mrow></math></span>. Gastineau and Togni conjectured that cubic graphs, except the Petersen and Tietze graphs, admit <span><math><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></mrow></math></span>-packing edge-colorings. In this paper, we prove that every claw-free cubic graph admits such a coloring.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"379 ","pages":"Pages 332-338"},"PeriodicalIF":1.0,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145049047","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}

{"title":"On the vertices belonging to all edge metric bases","authors":"Anni Hakanen ,&nbsp;Ville Junnila ,&nbsp;Tero Laihonen ,&nbsp;Ismael G. Yero","doi":"10.1016/j.dam.2025.08.054","DOIUrl":"10.1016/j.dam.2025.08.054","url":null,"abstract":"<div><div>An edge metric basis of a connected graph <span><math><mi>G</mi></math></span> is a smallest possible set of vertices <span><math><mi>S</mi></math></span> of <span><math><mi>G</mi></math></span> satisfying the following: for any two edges <span><math><mrow><mi>e</mi><mo>,</mo><mi>f</mi></mrow></math></span> of <span><math><mi>G</mi></math></span> there is a vertex <span><math><mrow><mi>s</mi><mo>∈</mo><mi>S</mi></mrow></math></span> such that the distances from <span><math><mi>s</mi></math></span> to <span><math><mi>e</mi></math></span> and <span><math><mi>f</mi></math></span> differ. The cardinality of an edge metric basis is the edge metric dimension of <span><math><mi>G</mi></math></span>. In this article we consider the existence of vertices in a graph <span><math><mi>G</mi></math></span> such that they must belong to each edge metric basis of <span><math><mi>G</mi></math></span>, and we call them <em>edge basis forced vertices</em>. On the other hand, we name <em>edge void vertices</em> those vertices which do not belong to any edge metric basis. Among other results, we first deal with the computational complexity of deciding whether a given vertex is an edge basis forced vertex or an edge void vertex. We also establish some tight bounds on the number of edge basis forced vertices of a graph, as well as, on the number of edges in a graph having at least one edge basis forced vertex. Moreover, we show some realization results concerning which values for the integers <span><math><mi>n</mi></math></span>, <span><math><mi>k</mi></math></span> and <span><math><mi>f</mi></math></span> allow to confirm the existence of a graph <span><math><mi>G</mi></math></span> with <span><math><mi>n</mi></math></span> vertices, <span><math><mi>f</mi></math></span> edge basis forced vertices and edge metric dimension <span><math><mi>k</mi></math></span>.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"379 ","pages":"Pages 339-354"},"PeriodicalIF":1.0,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145049048","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}

{"title":"Locating eigenvalues of matrogenic graphs in linear time","authors":"Nelson Assis Junior,&nbsp;Vilmar Trevisan","doi":"10.1016/j.dam.2025.08.050","DOIUrl":"10.1016/j.dam.2025.08.050","url":null,"abstract":"<div><div>Using a decomposition due to Tyshkevich, we proved that matrogenic graphs have clique-width at most 4 and this allowed us to compute, in linear time, some of spectral parameters, such as the spectral radius and the algebraic connectivity, for subfamilies of these graphs. This was achieved using the Diagonalize Algorithm developed by M. Fürer et al. in 2019. The techniques applied here may provide valuable tools to further explore spectral properties of matrogenic graphs and related graph classes as well.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"379 ","pages":"Pages 316-331"},"PeriodicalIF":1.0,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145027003","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}

{"title":"On obtaining long m-sequences from low-degree primitive polynomials","authors":"Dimitri Kagaris","doi":"10.1016/j.dam.2025.08.058","DOIUrl":"10.1016/j.dam.2025.08.058","url":null,"abstract":"<div><div>Maximum-length sequences of length <span><math><mrow><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msup><mo>−</mo><mn>1</mn></mrow></math></span> (m-sequences) are typically obtained by starting from a primitive polynomial of degree <span><math><mi>n</mi></math></span> over <span><math><mrow><mi>G</mi><mi>F</mi><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span> and configuring a Linear Feedback Shift Register (LFSR) based on that polynomial. In this study, we investigate the generation of <em>long</em> m-sequences based on a primitive polynomial of <em>low</em> degree. Specifically, we investigate a very simple form of an LFSR structure, referred to as <em>Two-Multiplier Split LFSR (2M-SLFSR)</em>, that consists of <span><math><mi>m</mi></math></span>\u0000 <span><math><mi>δ</mi></math></span>-bit cells and is based on a single low-degree primitive polynomial of degree <span><math><mrow><mi>δ</mi><mo>≥</mo><mn>2</mn></mrow></math></span> over <span><math><mrow><mi>G</mi><mi>F</mi><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span> and which can generate, with proper configuration, an m-sequence of length <span><math><mrow><msup><mrow><mn>2</mn></mrow><mrow><mi>m</mi><mi>δ</mi></mrow></msup><mo>−</mo><mn>1</mn></mrow></math></span>. For example, we show that starting from the primitive polynomial <span><math><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mi>x</mi><mo>+</mo><mn>1</mn></mrow></math></span> over <span><math><mrow><mi>G</mi><mi>F</mi><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span>, a 2M-SLFSR with <span><math><mrow><mi>m</mi><mo>=</mo><mn>599</mn></mrow></math></span> 2-bit cells can be constructed that yields an m-sequence of length <span><math><mrow><msup><mrow><mn>2</mn></mrow><mrow><mn>1198</mn></mrow></msup><mo>−</mo><mn>1</mn></mrow></math></span>. M-sequences of large length such as <span><math><mrow><msup><mrow><mn>2</mn></mrow><mrow><mn>512</mn></mrow></msup><mo>−</mo><mn>1</mn></mrow></math></span> obtained from low degree primitive polynomials via LFSR structures akin to 2M-SLFSR find current applications in stream ciphers like those used in SNOW-V and SNOW-Vi.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"379 ","pages":"Pages 272-287"},"PeriodicalIF":1.0,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145019021","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}

{"title":"The minimum number of maximal dissociation sets in unicyclic graphs","authors":"Junxia Zhang ,&nbsp;Xiangyu Ren ,&nbsp;Maoqun Wang","doi":"10.1016/j.dam.2025.08.053","DOIUrl":"10.1016/j.dam.2025.08.053","url":null,"abstract":"<div><div>A subset of vertices in a graph <span><math><mi>G</mi></math></span> is considered a maximal dissociation set if it induces a subgraph with vertex degree at most 1 and it is not contained within any other dissociation sets. In this paper, we show that every unicyclic graph of order <span><math><mi>n</mi></math></span> with <span><math><mrow><mi>n</mi><mo>≥</mo><mn>3</mn></mrow></math></span> contains at least <span><math><mrow><mrow><mo>⌊</mo><mfrac><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>⌋</mo></mrow><mo>+</mo><mn>2</mn></mrow></math></span> maximal dissociation sets. We also characterize the graphs attaining this lower bound.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"378 ","pages":"Pages 627-634"},"PeriodicalIF":1.0,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145019115","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}

{"title":"Conditional matching preclusion of enhanced hypercubes","authors":"Luyao Zhang,&nbsp;Xiaomin Hu,&nbsp;Shuang Zhao,&nbsp;Weihua Yang","doi":"10.1016/j.dam.2025.08.057","DOIUrl":"10.1016/j.dam.2025.08.057","url":null,"abstract":"<div><div>The conditional matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph with no isolated vertices that has neither perfect matchings nor almost perfect matchings. In this paper, we prove that the <span><math><mi>n</mi></math></span>-dimensional enhanced hypercubes are super conditional matched with <span><math><mrow><mi>n</mi><mo>≥</mo><mn>6</mn></mrow></math></span>. Our work is complementary to Lin et al. and Wang et al., who proved a special case of enhanced hypercubes is super conditional matched and calculated the conditional matching preclusion number of enhanced hypercubes, respectively.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"378 ","pages":"Pages 614-620"},"PeriodicalIF":1.0,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145018409","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}

{"title":"On the construction of xor-magic graphs","authors":"Ahmet Batal","doi":"10.1016/j.dam.2025.08.055","DOIUrl":"10.1016/j.dam.2025.08.055","url":null,"abstract":"<div><div>A simple connected graph of order <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msup></math></span> is defined as a xor-magic graph of power <span><math><mi>n</mi></math></span> if its vertices can be labeled with vectors from <span><math><msubsup><mrow><mi>F</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msubsup></math></span> in a one-to-one manner such that the sum of labels in each closed neighborhood set of vertices equals zero. In this paper, we introduce a method called the self-switching operation, which, when properly applied to an odd xor-magic graph of power <span><math><mi>n</mi></math></span>, generates a xor-magic graph of power <span><math><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></math></span>. We demonstrate the existence of a proper self-switching operation for any given odd xor-magic graph and provide a characterization of the cut space of a connected graph in the process. We also observe that the Dyck graph can be obtained from the complete graph of order 4 by applying three successive self-switching operations. Additionally, we investigate various graph products, including Cartesian, tensor, strong, lexicographical, and modular products. We observe that these products allow us to generate xor-magic graphs by selecting appropriate factor graphs. Notably, we discover that a modular product of graphs is always a xor-magic graph when the orders of its factors are powers of 2 (except for 2 itself). In the process, we realize that the Clebsch graph is the modular product of the cycle graph and the empty graph, each of order 4. By combining the self-switching operation with the modular product, we establish the existence of <span><math><mi>k</mi></math></span>-regular xor-magic graphs of power <span><math><mi>n</mi></math></span> for all <span><math><mrow><mi>n</mi><mo>≥</mo><mn>2</mn></mrow></math></span> and for all <span><math><mrow><mi>k</mi><mo>∈</mo><mrow><mo>{</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mo>…</mo><mo>,</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msup><mtext>-</mtext><mn>5</mn><mo>}</mo></mrow><mo>∪</mo><mrow><mo>{</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msup><mspace></mspace><mtext>-</mtext><mspace></mspace><mn>1</mn><mo>}</mo></mrow></mrow></math></span>. We also prove that there is no (<span><math><mrow><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msup><mspace></mspace><mtext>-</mtext><mspace></mspace><mn>3</mn></mrow></math></span>)-regular xor-magic graph of power <span><math><mi>n</mi></math></span>. Lastly, we introduce two more methods to produce xor-magic graphs. One method utilizes Cayley graphs and the other utilizes linear algebra.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"379 ","pages":"Pages 288-315"},"PeriodicalIF":1.0,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145019022","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}

{"title":"A characterization of minimally connected graphs without 2-clique cutsets","authors":"Hengzhe Li,&nbsp;Qiong Wang","doi":"10.1016/j.dam.2025.08.059","DOIUrl":"10.1016/j.dam.2025.08.059","url":null,"abstract":"<div><div>Clique cutsets are an important tool for studying both graph decomposition and graph characterization. For an integer <span><math><mrow><mi>k</mi><mo>≥</mo><mn>1</mn></mrow></math></span>, a <span><math><mi>k</mi></math></span>-<em>clique cutset</em> of a connected graph is a <span><math><mi>k</mi></math></span>-clique whose removal disconnects the graph. The family of minimally connected graphs without 1-clique cutsets is just the family of minimally 2-connected graphs, which was characterized by Dirac in 1967. Dirac also proved that each minimally 2-connected graph has no triangles. In this paper, we characterize the family of minimally connected graphs without 2-clique cutsets, and show that each minimally connected graph without 2-clique cutsets also has no triangles.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"378 ","pages":"Pages 621-626"},"PeriodicalIF":1.0,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145019114","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}