{"title":"Conditional matching preclusion of enhanced hypercubes","authors":"Luyao Zhang, Xiaomin Hu, Shuang Zhao, 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, 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}
Nicholas R. Beaton , Kai Ishihara , Mahshid Atapour , Jeremy W. Eng , Mariel Vazquez , Koya Shimokawa , Christine E. Soteros
{"title":"Entanglement statistics of polymers in a lattice tube and unknotting of 4-plats","authors":"Nicholas R. Beaton , Kai Ishihara , Mahshid Atapour , Jeremy W. Eng , Mariel Vazquez , Koya Shimokawa , Christine E. Soteros","doi":"10.1016/j.dam.2025.08.042","DOIUrl":"10.1016/j.dam.2025.08.042","url":null,"abstract":"<div><div>The Knot Entropy Conjecture states that the exponential growth rate of the number of <span><math><mi>n</mi></math></span>-edge lattice polygons with knot-type <span><math><mi>K</mi></math></span> is the same as that for unknot polygons. Moreover, the next order growth follows a power law in <span><math><mi>n</mi></math></span> with an exponent that increases by one for each prime knot in the knot decomposition of <span><math><mi>K</mi></math></span>. We provide the first proof of this conjecture by considering knots and non-split links in tube <span><math><msup><mrow><mi>T</mi></mrow><mrow><mo>∗</mo></mrow></msup></math></span>, an <span><math><mrow><mi>∞</mi><mo>×</mo><mn>2</mn><mo>×</mo><mn>1</mn></mrow></math></span> sublattice of the simple cubic lattice. We establish upper and lower bounds relating the asymptotics of the number of <span><math><mi>n</mi></math></span>-edge polygons with fixed link-type in <span><math><msup><mrow><mi>T</mi></mrow><mrow><mo>∗</mo></mrow></msup></math></span> to that of the number of <span><math><mi>n</mi></math></span>-edge unknots. For the upper bound, we prove that polygons can be unknotted by braid insertions. For the lower bound, we prove a pattern theorem for unknots using information from exact transfer-matrices. This work provides new knot theory results for 4-plats and new combinatorics results for lattice polygons. Connections to modelling polymers such as DNA in nanochannels are highlighted.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"379 ","pages":"Pages 242-271"},"PeriodicalIF":1.0,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144988113","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 topology diameters of the asymmetric cluster affinity cost","authors":"Paweł Górecki , Sanket Wagle , Oliver Eulenstein","doi":"10.1016/j.dam.2025.08.047","DOIUrl":"10.1016/j.dam.2025.08.047","url":null,"abstract":"<div><div>The asymmetric cluster affinity cost is based on the classic Robinson–Foulds metric and offers a more nuanced comparison of ordered tree pairs. When comparing the costs of these pairs, it is important to consider topology diameters to ensure a meaningful evaluation. The topology diameters of a cost represent the maximum values across all ordered tree pairs when the topology of either the first tree, the second tree, or both is fixed. This theoretical work outlines all topology diameters for the asymmetric cluster affinity cost and describes a linear-time algorithm that generates trees achieving the topology diameter for a given ordered pair of topologies. Our detailed experimental studies suggest that normalization strategies based on topology diameters can significantly improve comparative studies using the asymmetric cluster affinity cost.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"378 ","pages":"Pages 602-613"},"PeriodicalIF":1.0,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144925175","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":"Strong matching preclusion for folded hypercubes","authors":"Zhicheng Lin, Ruizhi Lin","doi":"10.1016/j.dam.2025.08.045","DOIUrl":"10.1016/j.dam.2025.08.045","url":null,"abstract":"<div><div>The strong matching preclusion number of <span><math><mi>G</mi></math></span> is the minimum number of vertices and edges whose deletion leaves the resulting graph without a perfect matching or an almost perfect matching. This concept was introduced by Park and Son to extending the classic matching preclusion problem. In this paper, we focus on strong matching preclusion for folded hypercube <span><math><mrow><mi>F</mi><msub><mrow><mi>Q</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></math></span>, an important variant of hypercube. We show that strong matching preclusion number of <span><math><mrow><mi>F</mi><msub><mrow><mi>Q</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></math></span> is <span><math><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></math></span> for even <span><math><mrow><mi>n</mi><mo>⩾</mo><mn>4</mn></mrow></math></span>.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"378 ","pages":"Pages 594-601"},"PeriodicalIF":1.0,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144925174","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":"Characterizing and transforming DAGs within the ℐ-lca framework","authors":"Marc Hellmuth, Anna Lindeberg","doi":"10.1016/j.dam.2025.08.037","DOIUrl":"10.1016/j.dam.2025.08.037","url":null,"abstract":"<div><div>We explore the connections between clusters and least common ancestors (LCAs) in directed acyclic graphs (DAGs), focusing on the interplay between so-called <span><math><mi>ℐ</mi></math></span>-lca-relevant DAGs and DAGs with the <span><math><mi>ℐ</mi></math></span>-lca-property. Here, <span><math><mi>ℐ</mi></math></span> denotes a set of integers. In <span><math><mi>ℐ</mi></math></span>-lca-relevant DAGs, each vertex is the unique LCA for some subset <span><math><mi>A</mi></math></span> of leaves of size <span><math><mrow><mrow><mo>|</mo><mi>A</mi><mo>|</mo></mrow><mo>∈</mo><mi>ℐ</mi></mrow></math></span>, whereas in a DAG with the <span><math><mi>ℐ</mi></math></span>-lca-property there exists a unique LCA for every subset <span><math><mi>A</mi></math></span> of leaves satisfying <span><math><mrow><mrow><mo>|</mo><mi>A</mi><mo>|</mo></mrow><mo>∈</mo><mi>ℐ</mi></mrow></math></span>. We elaborate on the difference between these two properties and establish their close relationship to pre-<span><math><mi>ℐ</mi></math></span>-ary and <span><math><mi>ℐ</mi></math></span>-ary set systems. This, in turn, generalizes results established for (pre-) binary and <span><math><mi>k</mi></math></span>-ary set systems. Moreover, we build upon recently established results that use a simple operator <span><math><mo>⊖</mo></math></span>, enabling the transformation of arbitrary DAGs into <span><math><mi>ℐ</mi></math></span>-lca-relevant DAGs. This process reduces unnecessary complexity while preserving key structural properties of the original DAG. The set <span><math><msub><mrow><mi>ℭ</mi></mrow><mrow><mi>G</mi></mrow></msub></math></span> consists of all clusters in a DAG <span><math><mi>G</mi></math></span>, where clusters correspond to the descendant leaves of vertices. While in some cases <span><math><mrow><msub><mrow><mi>ℭ</mi></mrow><mrow><mi>H</mi></mrow></msub><mo>=</mo><msub><mrow><mi>ℭ</mi></mrow><mrow><mi>G</mi></mrow></msub></mrow></math></span> when transforming <span><math><mi>G</mi></math></span> into an <span><math><mi>ℐ</mi></math></span>-lca-relevant DAG <span><math><mi>H</mi></math></span>, it often happens that certain clusters in <span><math><msub><mrow><mi>ℭ</mi></mrow><mrow><mi>G</mi></mrow></msub></math></span> do not appear as clusters in <span><math><mi>H</mi></math></span>. To understand this phenomenon in detail, we characterize the subset of clusters in <span><math><msub><mrow><mi>ℭ</mi></mrow><mrow><mi>G</mi></mrow></msub></math></span> that remain in <span><math><mi>H</mi></math></span> for DAGs <span><math><mi>G</mi></math></span> with the <span><math><mi>ℐ</mi></math></span>-lca-property. Furthermore, we show that the set <span><math><mi>W</mi></math></span> of vertices required to transform <span><math><mi>G</mi></math></span> into <span><math><mrow><mi>H</mi><mo>=</mo><mi>G</mi><mo>⊖</mo><mi>W</mi></mrow></math></span> is uniquely determined for such DAGs. This, in turn, allows us to show that the “shortcut-free” versi","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"378 ","pages":"Pages 584-593"},"PeriodicalIF":1.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144921644","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}
Florian Hörsch , Benjamin Peyrille , Zoltán Szigeti
{"title":"Matroid-reachability-based decomposition into arborescences","authors":"Florian Hörsch , Benjamin Peyrille , Zoltán Szigeti","doi":"10.1016/j.dam.2025.08.036","DOIUrl":"10.1016/j.dam.2025.08.036","url":null,"abstract":"<div><div>The problem of complete matroid-reachability-based packing of arborescences was solved by Király. Here we solve the corresponding decomposition problem that turns out to be more complicated. The result is obtained from the solution of the more general problem of matroid-reachability-based <span><math><mrow><mo>(</mo><mi>ℓ</mi><mo>,</mo><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>)</mo></mrow></math></span>-limited packing of arborescences where we are given a lower bound <span><math><mi>ℓ</mi></math></span> and an upper bound <span><math><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span> on the total number of arborescences in the packing. The problem is considered for branchings as well.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"378 ","pages":"Pages 568-583"},"PeriodicalIF":1.0,"publicationDate":"2025-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144913552","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}
Subhadeep R. Dev , Sanjana Dey , Florent Foucaud , Krishna Narayanan , Lekshmi Ramasubramony Sulochana
{"title":"Monitoring edge-geodetic sets in graphs","authors":"Subhadeep R. Dev , Sanjana Dey , Florent Foucaud , Krishna Narayanan , Lekshmi Ramasubramony Sulochana","doi":"10.1016/j.dam.2025.08.041","DOIUrl":"10.1016/j.dam.2025.08.041","url":null,"abstract":"<div><div>We introduce a new graph-theoretic concept in the area of network monitoring. In this area, one wishes to monitor the vertices and/or the edges of a network (viewed as a graph) in order to detect and prevent failures. Inspired by two notions studied in the literature (edge-geodetic sets and distance-edge-monitoring sets), we define the notion of a monitoring edge-geodetic set (MEG-set for short) of a graph <span><math><mi>G</mi></math></span> as an edge-geodetic set <span><math><mrow><mi>S</mi><mo>⊆</mo><mi>V</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> of <span><math><mi>G</mi></math></span> (that is, every edge of <span><math><mi>G</mi></math></span> lies on some shortest path between two vertices of <span><math><mi>S</mi></math></span>) with the additional property that for every edge <span><math><mi>e</mi></math></span> of <span><math><mi>G</mi></math></span>, there is a vertex pair <span><math><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow></math></span> of <span><math><mi>S</mi></math></span> such that <span><math><mi>e</mi></math></span> lies on <em>all</em> shortest paths between <span><math><mi>x</mi></math></span> and <span><math><mi>y</mi></math></span>. The motivation is that, if some edge <span><math><mi>e</mi></math></span> is removed from the network (for example if it ceases to function), the monitoring probes <span><math><mi>x</mi></math></span> and <span><math><mi>y</mi></math></span> will detect the failure since the distance between them will increase.</div><div>We explore the notion of MEG-sets by deriving the minimum size of a MEG-set for some basic graph classes (trees, cycles, unicyclic graphs, complete graphs, grids, hypercubes, corona products...) and we prove an upper bound using the feedback edge set of the graph.</div><div>We also show that determining the smallest size of an MEG-set of a graph is NP-hard, even for graphs of maximum degree at most 9.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"377 ","pages":"Pages 598-610"},"PeriodicalIF":1.0,"publicationDate":"2025-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144911854","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":"Fair link contributions for values of network cooperative games","authors":"Daniel Li Li , Erfang Shan","doi":"10.1016/j.dam.2025.08.044","DOIUrl":"10.1016/j.dam.2025.08.044","url":null,"abstract":"<div><div>A network game <span><math><mrow><mo>(</mo><mi>N</mi><mo>,</mo><mi>v</mi><mo>,</mo><mi>L</mi><mo>)</mo></mrow></math></span> consists of a cooperative game <span><math><mrow><mo>(</mo><mi>N</mi><mo>,</mo><mi>v</mi><mo>)</mo></mrow></math></span> and a network <span><math><mrow><mo>(</mo><mi>N</mi><mo>,</mo><mi>L</mi><mo>)</mo></mrow></math></span>, in which the formation of coalitions of players is restricted by <span><math><mi>L</mi></math></span> and links in <span><math><mi>L</mi></math></span> signify communication between players. Two well-known allocation rules for network games are the Myerson value and the position value, the latter of which is defined on the network game <span><math><mrow><mo>(</mo><mi>N</mi><mo>,</mo><mi>v</mi><mo>,</mo><mi>L</mi><mo>)</mo></mrow></math></span> where the underlying game <span><math><mrow><mo>(</mo><mi>N</mi><mo>,</mo><mi>v</mi><mo>)</mo></mrow></math></span> is zero-normalized. In this paper we propose new axiomatic characterizations of the Myerson value. Furthermore, we define a new position value without restriction of zero-normalization on game <span><math><mrow><mo>(</mo><mi>N</mi><mo>,</mo><mi>v</mi><mo>)</mo></mrow></math></span> and establish a characterization of the position value.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"379 ","pages":"Pages 236-241"},"PeriodicalIF":1.0,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144913673","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}
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