This work addresses the inverse Cauchy problem for the modified Helmholtz equation using an alternating iterative approach. The central contribution lies in the design of novel local error indicators based on a posteriori analysis, which simultaneously assess the accuracy of the spatial discretization and the convergence behavior of the iterative algorithm. Unlike standard methods, our strategy leverages a comparative assessment of these indicators to drive an adaptive mesh refinement process. This adaptive framework ensures a more balanced distribution of computational resources, significantly reducing the numerical cost while maintaining high solution accuracy. The proposed methodology is validated through a series of synthetic and application-driven numerical experiments, demonstrating both its effectiveness and robustness in reconstructing inaccessible boundary data.
{"title":"A posteriori-driven adaptive strategy for solving inverse Cauchy problems in diffusion-reaction models","authors":"Hafida Hamdi , Mourad Nachaoui , Amal Bergam , Abdeljalil Nachaoui","doi":"10.1016/j.amc.2025.129902","DOIUrl":"10.1016/j.amc.2025.129902","url":null,"abstract":"<div><div>This work addresses the inverse Cauchy problem for the modified Helmholtz equation using an alternating iterative approach. The central contribution lies in the design of novel local error indicators based on a posteriori analysis, which simultaneously assess the accuracy of the spatial discretization and the convergence behavior of the iterative algorithm. Unlike standard methods, our strategy leverages a comparative assessment of these indicators to drive an adaptive mesh refinement process. This adaptive framework ensures a more balanced distribution of computational resources, significantly reducing the numerical cost while maintaining high solution accuracy. The proposed methodology is validated through a series of synthetic and application-driven numerical experiments, demonstrating both its effectiveness and robustness in reconstructing inaccessible boundary data.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"518 ","pages":"Article 129902"},"PeriodicalIF":3.4,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145814360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper addresses the exponential stabilization of nonlinear stochastic Markovian jump systems (NSMJSs) based on stochastic feedback sampled-data controllers. Firstly, a stochastic sampled-data-based switching control framework is established for NSMJSs, in which the switching controller modes do not match the system mode. The advantages are that it does not require real-time detection of system modes and relaxes the strict condition that the system mode remains unchanged between the sampling intervals. Secondly, a novel sampling sub-interval error analysis method is developed for the design of the stochastic feedback sampling controller, such that the NSMJSs are -th exponentially stable, and the conditions for the maximum allowable upper bound of sampling intervals (UBOSIs) are achieved, which can not only increase the sampling intervals significantly but also decrease the computation resource. Moreover, some enhanced -th exponential stabilization results for general stochastic systems are given. Compared with some existing important results, the conservatism of the UBOSIs is reduced greatly by simulation examples.
{"title":"A sampling sub-interval error-based stochastic feedback sampled-data control for nonlinear stochastic Markovian jump systems","authors":"Yingchun Wang, Siyong Song, Yunfei Mu, Huaguang Zhang","doi":"10.1016/j.amc.2025.129895","DOIUrl":"10.1016/j.amc.2025.129895","url":null,"abstract":"<div><div>This paper addresses the exponential stabilization of nonlinear stochastic Markovian jump systems (NSMJSs) based on stochastic feedback sampled-data controllers. Firstly, a stochastic sampled-data-based switching control framework is established for NSMJSs, in which the switching controller modes do not match the system mode. The advantages are that it does not require real-time detection of system modes and relaxes the strict condition that the system mode remains unchanged between the sampling intervals. Secondly, a novel sampling sub-interval error analysis method is developed for the design of the stochastic feedback sampling controller, such that the NSMJSs are <span><math><mi>p</mi></math></span>-th exponentially stable, and the conditions for the maximum allowable upper bound of sampling intervals (UBOSIs) are achieved, which can not only increase the sampling intervals significantly but also decrease the computation resource. Moreover, some enhanced <span><math><mi>p</mi></math></span>-th exponential stabilization results for general stochastic systems are given. Compared with some existing important results, the conservatism of the UBOSIs is reduced greatly by simulation examples.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"517 ","pages":"Article 129895"},"PeriodicalIF":3.4,"publicationDate":"2025-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145813782","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-20DOI: 10.1016/j.amc.2025.129896
Jing Ye , Miaomiao Han , Murong Xu
Bernshteyn and Lee introduced weak degeneracy, showing that its value plus one bounds various graph coloring parameters. In this paper, we prove that if G is a planar graph with maximum degree Δ and girth g, then weak degeneracy holds independently under each of the following conditions: (i) Δ ≥ 16 and ; (ii) Δ ≥ 10 and 8 ≤ g ≤ 9; (iii) Δ ≥ 6 and 10 ≤ g ≤ 11; (iv) and g ≥ 12. This work generalizes the results obtained by Ivanova in [Journal of Applied and Industrial Mathematics, 5(2)(2011), 221–230].
Bernshteyn和Lee引入了弱简并性，证明了它的值加上一个边界的各种图着色参数。在本文中，我们证明了如果G是一个最大度数Δ，周长G的平面图，那么弱简并度wd(G2)=Δ在以下条件下独立成立：(i) Δ ≥ 16且G =7；（ii） Δ ≥ 10和8 ≤ g ≤ 9；（iii） Δ ≥ 6和10 ≤ g ≤ 11；（iv） Δ=5, g ≥ 本文推广了Ivanova在[应用与工业数学学报，5(2)(2011)，221-230]中得到的结果。
{"title":"Weak degeneracy of the square of planar graphs with given girth","authors":"Jing Ye , Miaomiao Han , Murong Xu","doi":"10.1016/j.amc.2025.129896","DOIUrl":"10.1016/j.amc.2025.129896","url":null,"abstract":"<div><div>Bernshteyn and Lee introduced weak degeneracy, showing that its value plus one bounds various graph coloring parameters. In this paper, we prove that if <em>G</em> is a planar graph with maximum degree Δ and girth <em>g</em>, then weak degeneracy <span><math><mrow><mi>w</mi><mi>d</mi><mo>(</mo><msup><mi>G</mi><mn>2</mn></msup><mo>)</mo><mo>=</mo><mstyle><mi>Δ</mi></mstyle></mrow></math></span> holds independently under each of the following conditions: (i) Δ ≥ 16 and <span><math><mrow><mi>g</mi><mo>=</mo><mn>7</mn></mrow></math></span>; (ii) Δ ≥ 10 and 8 ≤ <em>g</em> ≤ 9; (iii) Δ ≥ 6 and 10 ≤ <em>g</em> ≤ 11; (iv) <span><math><mrow><mstyle><mi>Δ</mi></mstyle><mo>=</mo><mn>5</mn></mrow></math></span> and <em>g</em> ≥ 12. This work generalizes the results obtained by Ivanova in [Journal of Applied and Industrial Mathematics, 5(2)(2011), 221–230].</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"517 ","pages":"Article 129896"},"PeriodicalIF":3.4,"publicationDate":"2025-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145786036","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-18DOI: 10.1016/j.amc.2025.129903
Jinlong Ma , Guanghui Wang
Memory effects of individuals have been demonstrated to significantly promote cooperation, attracting widespread attention among scholars exploring the underlying dynamics of cooperative behavior. In this paper, we build a strategy updating framework by proposing a neighbor screening mechanism and combining particle swarm optimization algorithm in memory-based evolutionary prisoners’ dilemma game. Under the proposed mechanism, individuals may not imitate a neighbor with the only highest payoff from the current round when updating their strategy. Instead, individual evaluates the historical performance by his/her neighbors’ the frequency of choosing cooperation strategy and being chosen as an optimal neighbor and screen out the neighbors who do not meet the defined initial threshold. Moreover, a threshold adjustment parameter α is introduced to strengthen the flexible of the threshold. In addition, the proposed mechanism is compared in two situations: fixed memory and dynamic memory. Specifically, in the neighbor screening mechanism with dynamic memory, each individual’s memory will decay or remain unchanged according to the relationship between their current payoff and average payoff of all players in the local group. The simulation results reveal that the advantages of short memory length and dynamic memory in promoting cooperation. Furthermore, the synergistic effect between initial threshold and memory length better promotes cooperation. Additionally, a slight increase in the threshold adjustment parameter α promotes cooperation when the initial threshold is low. These findings shed light on how cooperation can be enhanced through specific rules.
{"title":"Memory-based evolutionary prisoner’s dilemma game with neighbor screening mechanism","authors":"Jinlong Ma , Guanghui Wang","doi":"10.1016/j.amc.2025.129903","DOIUrl":"10.1016/j.amc.2025.129903","url":null,"abstract":"<div><div>Memory effects of individuals have been demonstrated to significantly promote cooperation, attracting widespread attention among scholars exploring the underlying dynamics of cooperative behavior. In this paper, we build a strategy updating framework by proposing a neighbor screening mechanism and combining particle swarm optimization algorithm in memory-based evolutionary prisoners’ dilemma game. Under the proposed mechanism, individuals may not imitate a neighbor with the only highest payoff from the current round when updating their strategy. Instead, individual evaluates the historical performance by his/her neighbors’ the frequency of choosing cooperation strategy and being chosen as an optimal neighbor and screen out the neighbors who do not meet the defined initial threshold. Moreover, a threshold adjustment parameter <em>α</em> is introduced to strengthen the flexible of the threshold. In addition, the proposed mechanism is compared in two situations: fixed memory and dynamic memory. Specifically, in the neighbor screening mechanism with dynamic memory, each individual’s memory will decay or remain unchanged according to the relationship between their current payoff and average payoff of all players in the local group. The simulation results reveal that the advantages of short memory length and dynamic memory in promoting cooperation. Furthermore, the synergistic effect between initial threshold and memory length better promotes cooperation. Additionally, a slight increase in the threshold adjustment parameter <em>α</em> promotes cooperation when the initial threshold is low. These findings shed light on how cooperation can be enhanced through specific rules.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"517 ","pages":"Article 129903"},"PeriodicalIF":3.4,"publicationDate":"2025-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145784752","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-18DOI: 10.1016/j.amc.2025.129869
Masood Ahmad , Kejia Pan , Siraj-ul-Islam
In this work, Haar wavelet methods are developed for the numerical solution of the two-dimensional Burgers’ equation and a system of Burgers’ equations. The highest derivatives involved in the governing equation are approximated using Haar wavelets, while temporal discretization is achieved using several schemes: the θ-weighted scheme, the fourth-order Runge–Kutta (RK4) scheme, the adaptive step-size Runge–Kutta schemes including Runge–Kutta 3(2) (RK32) and the Runge–Kutta–Fehlberg (RKF45) as well as a strong stability-preserving Runge–Kutta (SSPRK(3,3)) scheme. To the best of our knowledge, this is the first matrix Haar wavelets formulation of the RK4, the RK32, the RKF45 and the SSPRK(3,3) schemes to two-dimensional time-dependent partial differential equations (PDEs). To reduce the size and complexity of the method, certain wavelet coefficients are deliberately omitted to reduce the size of the algebraic system of equations. The Kronecker product and vectorization operators are employed in the Runge–Kutta schemes to significantly reduce the computational cost of matrix operations. This strategy enhances the efficiency of the Runge–Kutta schemes compared to both the θ-weighted scheme and other methods reported in the literature. The proposed methods are assessed in terms of accuracy, spatial convergence rate, and computational cost. Comparative results demonstrate that the proposed schemes are both robust and computationally efficient.
{"title":"Solving Burgers’ equations with a new Haar wavelet approach: An application of Kronecker product and vectorization","authors":"Masood Ahmad , Kejia Pan , Siraj-ul-Islam","doi":"10.1016/j.amc.2025.129869","DOIUrl":"10.1016/j.amc.2025.129869","url":null,"abstract":"<div><div>In this work, Haar wavelet methods are developed for the numerical solution of the two-dimensional Burgers’ equation and a system of Burgers’ equations. The highest derivatives involved in the governing equation are approximated using Haar wavelets, while temporal discretization is achieved using several schemes: the <em>θ</em>-weighted scheme, the fourth-order Runge–Kutta (RK4) scheme, the adaptive step-size Runge–Kutta schemes including Runge–Kutta 3(2) (RK32) and the Runge–Kutta–Fehlberg (RKF45) as well as a strong stability-preserving Runge–Kutta (SSPRK(3,3)) scheme. To the best of our knowledge, this is the first matrix Haar wavelets formulation of the RK4, the RK32, the RKF45 and the SSPRK(3,3) schemes to two-dimensional time-dependent partial differential equations (PDEs). To reduce the size and complexity of the method, certain wavelet coefficients are deliberately omitted to reduce the size of the algebraic system of equations. The Kronecker product and vectorization operators are employed in the Runge–Kutta schemes to significantly reduce the computational cost of matrix operations. This strategy enhances the efficiency of the Runge–Kutta schemes compared to both the <em>θ</em>-weighted scheme and other methods reported in the literature. The proposed methods are assessed in terms of accuracy, spatial convergence rate, and computational cost. Comparative results demonstrate that the proposed schemes are both robust and computationally efficient.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"517 ","pages":"Article 129869"},"PeriodicalIF":3.4,"publicationDate":"2025-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145798793","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-18DOI: 10.1016/j.amc.2025.129900
Changhao Li , Yingnan Pan , Xingjian Sun
Till now, there are many investigations on networked control systems (NCSs) with event-triggering weighted-try-once-discard protocol (ET-WTODP) and attack compensation mechanism, but targeted improvements from the perspective of network resource utilization and control performance still require further exploration. This paper studies the design issue of interval type-2 fuzzy security controller for NCSs with improved ET-WTODP and denial-of-service (DoS) attacks compensation mechanism. Firstly, in order to better schedule the operating states of ET-WTODP, an improved ET-WTODP is designed. In contrast with existing ET-WTODPs, the improved ET-WTODP can be more flexible to schedule the operating states through the change trends of system states, which provides better network resource utilization efficiency. Secondly, an improved DoS attacks compensation mechanism is designed to further reduce the adverse impact of DoS attacks by predicting the output of the controller when attacks occur. Taking ET-WTODP and DoS attacks compensation mechanism into account, sufficient conditions for the stochastic stability of closed-loop system under H∞ performance are obtained based on Lyapunov stability theory. Finally, simulation verification is utilized to testify the effectiveness of the proposed control method.
{"title":"Protocol-based security controller design for networked control systems with DoS attacks compensation mechanism","authors":"Changhao Li , Yingnan Pan , Xingjian Sun","doi":"10.1016/j.amc.2025.129900","DOIUrl":"10.1016/j.amc.2025.129900","url":null,"abstract":"<div><div>Till now, there are many investigations on networked control systems (NCSs) with event-triggering weighted-try-once-discard protocol (ET-WTODP) and attack compensation mechanism, but targeted improvements from the perspective of network resource utilization and control performance still require further exploration. This paper studies the design issue of interval type-2 fuzzy security controller for NCSs with improved ET-WTODP and denial-of-service (DoS) attacks compensation mechanism. Firstly, in order to better schedule the operating states of ET-WTODP, an improved ET-WTODP is designed. In contrast with existing ET-WTODPs, the improved ET-WTODP can be more flexible to schedule the operating states through the change trends of system states, which provides better network resource utilization efficiency. Secondly, an improved DoS attacks compensation mechanism is designed to further reduce the adverse impact of DoS attacks by predicting the output of the controller when attacks occur. Taking ET-WTODP and DoS attacks compensation mechanism into account, sufficient conditions for the stochastic stability of closed-loop system under <em>H</em><sub>∞</sub> performance are obtained based on Lyapunov stability theory. Finally, simulation verification is utilized to testify the effectiveness of the proposed control method.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"517 ","pages":"Article 129900"},"PeriodicalIF":3.4,"publicationDate":"2025-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145784750","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-18DOI: 10.1016/j.amc.2025.129897
Donghao Xu , Yanyi Nie , Tao Lin
The rapid globalization and expansion of transportation networks have significantly increased cross-regional population mobility, contributing to the frequent re-emergence of pandemics. Alongside viral mutations and immune escape, these factors complicate epidemic control. Within a meta-population framework in this study, we propose a dual-intervention model that combines regional containment strategies with strain evolution dynamics to explore how these interventions influence both infection spread and strain diversity. Our simulations reveal that while strain-targeted interventions moderate infection densities, they inadvertently trigger compensatory growth of non-targeted dominant strains. Regional interventions in high-density areas effectively lower infection levels, but they have a limited impact on controlling strain diversity. In contrast, our dual-intervention model, which addresses both spatial and evolutionary aspects, reduces the spread of dominant strains, lowers overall infection rates, and offers a more effective strategy for managing harmful variants.
{"title":"Exploring the effectiveness of coupled control measures on strain diversity and epidemic spread","authors":"Donghao Xu , Yanyi Nie , Tao Lin","doi":"10.1016/j.amc.2025.129897","DOIUrl":"10.1016/j.amc.2025.129897","url":null,"abstract":"<div><div>The rapid globalization and expansion of transportation networks have significantly increased cross-regional population mobility, contributing to the frequent re-emergence of pandemics. Alongside viral mutations and immune escape, these factors complicate epidemic control. Within a meta-population framework in this study, we propose a dual-intervention model that combines regional containment strategies with strain evolution dynamics to explore how these interventions influence both infection spread and strain diversity. Our simulations reveal that while strain-targeted interventions moderate infection densities, they inadvertently trigger compensatory growth of non-targeted dominant strains. Regional interventions in high-density areas effectively lower infection levels, but they have a limited impact on controlling strain diversity. In contrast, our dual-intervention model, which addresses both spatial and evolutionary aspects, reduces the spread of dominant strains, lowers overall infection rates, and offers a more effective strategy for managing harmful variants.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"517 ","pages":"Article 129897"},"PeriodicalIF":3.4,"publicationDate":"2025-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145784751","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-16DOI: 10.1016/j.amc.2025.129808
Štefan Berežný , Tomáš Madaras , Daniela Matisová , Juraj Valiska
A path P in a drawing of a graph G with a given rotation system is called an anti-A-path if no two consecutive edges of P are consecutive in the local rotation of edges around their common vertex. G is anti-A-connected if every pair of its vertices can be connected by an anti-A-path. We investigate anti-A-connectedness in plane graphs of minimum degree 5, aiming to find, with the computer support, the graphs not sharing this property. On the other hand, we show that several large families of polyhedral graphs are anti-A-connected.
{"title":"On anti-A-connectivity in plane graphs","authors":"Štefan Berežný , Tomáš Madaras , Daniela Matisová , Juraj Valiska","doi":"10.1016/j.amc.2025.129808","DOIUrl":"10.1016/j.amc.2025.129808","url":null,"abstract":"<div><div>A path <em>P</em> in a drawing of a graph <em>G</em> with a given rotation system is called an anti-A-path if no two consecutive edges of <em>P</em> are consecutive in the local rotation of edges around their common vertex. <em>G</em> is anti-A-connected if every pair of its vertices can be connected by an anti-A-path. We investigate anti-A-connectedness in plane graphs of minimum degree 5, aiming to find, with the computer support, the graphs not sharing this property. On the other hand, we show that several large families of polyhedral graphs are anti-A-connected.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"517 ","pages":"Article 129808"},"PeriodicalIF":3.4,"publicationDate":"2025-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145784755","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-15DOI: 10.1016/j.amc.2025.129898
Huaihe Huang , Ye Ye , Wei Bao , Yue Zhang , Nenggang Xie
{"title":"Corrigendum to “An Evolutionary Game Analysis of a Dynamically Switching Zero-Determinant Strategy” [Applied Mathematics and Computation 515 (2026) 129862]","authors":"Huaihe Huang , Ye Ye , Wei Bao , Yue Zhang , Nenggang Xie","doi":"10.1016/j.amc.2025.129898","DOIUrl":"10.1016/j.amc.2025.129898","url":null,"abstract":"","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"516 ","pages":"Article 129898"},"PeriodicalIF":3.4,"publicationDate":"2025-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145753420","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-10DOI: 10.1016/j.amc.2025.129893
Xiaoqian Zhang, Weijun Liu, Lu Lu
The distance splitting field of distance matrix associated with a graph is the smallest field extension of that contains all of its distance eigenvalues. The extension degree is called its distance algebraic degree. A graph Γ is called k-distance integral if distance algebraic degree is equal to k. In this paper, we prove that the normal Cayley graph is distance algebraically integral over field K if and only if it is algebraically integral over K, and the Cayley graphs over cyclic groups is 2-distance integral if and only if it is 2-integral. Moreover, we construct k-distance integral Cayley graphs over cyclic groups, and classify the 2-distance integral abelian Cayley graphs with valency 2, 3, 4 and 5.
{"title":"On 2-distance integral Cayley graphs","authors":"Xiaoqian Zhang, Weijun Liu, Lu Lu","doi":"10.1016/j.amc.2025.129893","DOIUrl":"10.1016/j.amc.2025.129893","url":null,"abstract":"<div><div>The distance splitting field of distance matrix associated with a graph is the smallest field extension of <span><math><mi>Q</mi></math></span> that contains all of its distance eigenvalues. The extension degree is called its distance algebraic degree. A graph Γ is called <em>k</em>-distance integral if distance algebraic degree is equal to <em>k</em>. In this paper, we prove that the normal Cayley graph is distance algebraically integral over field <em>K</em> if and only if it is algebraically integral over <em>K</em>, and the Cayley graphs over cyclic groups is 2-distance integral if and only if it is 2-integral. Moreover, we construct <em>k</em>-distance integral Cayley graphs over cyclic groups, and classify the 2-distance integral abelian Cayley graphs with valency 2, 3, 4 and 5.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"517 ","pages":"Article 129893"},"PeriodicalIF":3.4,"publicationDate":"2025-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145712288","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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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