Applied Mathematics and Computation最新文献

{"title":"Exploring transient neurophysiological states through local and time-varying measures of information dynamics","authors":"Yuri Antonacci ,&nbsp;Chiara Barà ,&nbsp;Giulio de Felice ,&nbsp;Antonino Sferlazza ,&nbsp;Riccardo Pernice ,&nbsp;Luca Faes","doi":"10.1016/j.amc.2025.129437","DOIUrl":"10.1016/j.amc.2025.129437","url":null,"abstract":"<div><h3>Background</h3><div>Studying the temporal evolution of complex systems requires tools able to quantify the strength of predictable dynamics within their output signals. Among information theoretic measures, information storage (IS) reflects the regularity of system dynamics by measuring the information shared between the present and the past system states.</div></div><div><h3>Methods</h3><div>While the conventional IS computation provides an overall measure of predictable information, transient behaviors of predictability occurring during system transitions can be assessed by time resolved measures such as the local information storage (L-IS) and the time-varying information storage (TV-IS).</div></div><div><h3>Results</h3><div>TV-IS tracks sudden changes of the information stored in the system, which is reflected in its average value computed over specific time intervals; on the other hand, the surprise originated by the emergence of a change in the predictability is reflected in the variance of the L-IS computed within specific time intervals. In neurophysiological applications, the distinct phenomena of respiratory activity in sleep apnea and brain activity during somatosensory stimulation both reveal a significant decrease of IS evoked by state transitions, highlighting how such transitions can inject new information in physiological systems, affecting significantly their internal dynamics.</div></div><div><h3>Conclusions</h3><div>TV-IS and L-IS provide different and complementary information about the behavior of the systems under investigation, thereby offering valuable tools for the study of complex physiological systems where both stationary and non-stationary conditions may be present.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"500 ","pages":"Article 129437"},"PeriodicalIF":3.5,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A fast implicit difference scheme with nonuniform discretized grids for the time-fractional Black–Scholes model","authors":"Qi Xin ,&nbsp;Xian-Ming Gu ,&nbsp;Li-Bin Liu","doi":"10.1016/j.amc.2025.129441","DOIUrl":"10.1016/j.amc.2025.129441","url":null,"abstract":"<div><div>The solution of the time-fractional Black–Scholes (TFBS) equation often exhibits a weak singularity at initial time and possible non-physical oscillations in the computed solution due to the degeneracy of the BS differential operator. To address this issue, we combine a modified graded mesh and a piecewise uniform mesh for temporal and spatial discretizations, respectively. Then we use the fast approximation (rather than the direct approximation) of the <em>L</em>1 scheme for the Caputo derivative to establish an implicit difference method for the TFBS model. Our analysis shows the stability and convergence of the proposed scheme, as well as the <em>α</em>-nonrobust error bounds. Finally, numerical results are presented to show the effectiveness of the proposed method.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"500 ","pages":"Article 129441"},"PeriodicalIF":3.5,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738706","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}

{"title":"Corrigendum to “Mathematical modeling of electro hydrodynamic non-Newtonian fluid flow through tapered arterial stenosis with periodic body acceleration and applied magnetic field” [Applied Mathematics and Computation, 362(2019) 124453]]","authors":"R. Padma ,&nbsp;R. Ponalagusamy ,&nbsp;R. Tamil Selvi","doi":"10.1016/j.amc.2025.129418","DOIUrl":"10.1016/j.amc.2025.129418","url":null,"abstract":"<div><div>A mathematical model is proposed to the pulsatile flow of blood in a tapered artery with mild constriction. This study considers blood as an electrically conducting, non-Newtonian fluid (Jeffrey fluid) which contains magnetic nanoparticles. As blood conducts electricity, it exerts an electric force along the flow direction due to the induced magnetic force by an applied magnetic field which produces Lorentz force and influences the fluidity. Assuming that the pulsatile fluid flow is accelerated by a body force that has in slip velocity at the wall, a set of coupled nonlinear Navier–Stokes equation governing the flow networks is obtained. By employing Laplace and Hankel transforms on the partial equations, we obtain an exact solution for the velocity of flow pattern. Further, the evaluated axial velocity of both fluid and particle are used to find the physiological quantities such as shear stress, flow resistivity and volume of fluid flow. Their dependency on the Womersley parameter, Hartmann number, shape parameter, Jeffrey number and electrokinetic number are calculated numerically and explained graphically. Furthermore, the results are compared within slip and no slip velocities.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"500 ","pages":"Article 129418"},"PeriodicalIF":3.5,"publicationDate":"2025-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143734614","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}

{"title":"Distance ideals of digraphs","authors":"Carlos A. Alfaro ,&nbsp;Teresa I. Hoekstra-Mendoza ,&nbsp;Juan Pablo Serrano ,&nbsp;Ralihe R. Villagrán","doi":"10.1016/j.amc.2025.129430","DOIUrl":"10.1016/j.amc.2025.129430","url":null,"abstract":"<div><div>We focus on strongly connected, strong for short, digraphs since in this setting distance is defined for every pair of vertices. Distance ideals generalize the spectrum and Smith normal form of several distance matrices associated with strong digraphs. We introduce the concept of pattern which allow us to characterize the family <span><math><msub><mrow><mi>Γ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> of digraphs with only one trivial distance ideal over <span><math><mi>Z</mi></math></span>. This result generalizes an analogous result for undirected graphs that states that connected graphs with one trivial ideal over <span><math><mi>Z</mi></math></span> consists of either complete graphs or complete bipartite graphs. It turns out that the strong digraphs in <span><math><msub><mrow><mi>Γ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> consists in the circuit with 3 vertices and a family Λ of strong digraphs that contains complete graphs and complete bipartite graphs, regarded as digraphs. We also compute all distance ideals of some strong digraphs in the family Λ. Then, we explore the distance ideals of circuits, which turns out to be an infinite family of digraphs with unbounded diameter in <span><math><msub><mrow><mi>Γ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>, that is, digraphs with two trivial distance ideals.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"500 ","pages":"Article 129430"},"PeriodicalIF":3.5,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143724617","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}

{"title":"Out-of-equilibrium inference of feeding rates through population data from generic consumer-resource stochastic dynamics","authors":"José A. Capitán ,&nbsp;David Alonso","doi":"10.1016/j.amc.2025.129434","DOIUrl":"10.1016/j.amc.2025.129434","url":null,"abstract":"<div><div>Statistical models are often structurally unidentifiable, because different sets of parameters can lead to equal model outcomes. To be useful for prediction and parameter inference from data, stochastic population models need to be identifiable, this meaning that model parameters can be uniquely inferred from a large number of model observations. In particular, precise estimation of feeding rates in consumer-resource dynamics is crucial, because consumer-resource processes are central in determining biomass transport across ecosystems. Model parameters are usually estimated at stationarity, because in that case model analyses are often easier. In this contribution we analyze the problem of parameter redundancy in a multi-resource consumer-resource model, showing that model identifiability depends on whether the dynamics have reached stationarity or not. To be precise, we: (i) Calculate the steady-state and out-of-equilibrium probability distributions of predator's abundances analytically using generating functions, which allow us to unveil parameter redundancy and carry out proper maximum likelihood estimation. (ii) Conduct <em>in silico</em> experiments by tracking the abundance of consumers that are either searching for or handling prey, data then used for maximum likelihood parameter estimation. (iii) Show that, when model observations are recorded out of equilibrium, feeding parameters are truly identifiable, whereas if sampling is done solely at stationarity, only ratios of rates can be inferred from data (i.e., parameters are redundant). We discuss the implications of our results when inferring parameters of general dynamical models.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"500 ","pages":"Article 129434"},"PeriodicalIF":3.5,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143725612","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}

{"title":"Parking triangles on a continuous ladder","authors":"Stjepan Šebek","doi":"10.1016/j.amc.2025.129431","DOIUrl":"10.1016/j.amc.2025.129431","url":null,"abstract":"<div><div>In this article we study a variant of the famous Rényi's car-parking problem in which we are parking isosceles triangles on a strip of height 1, and where the base of the triangle can be on either side of that strip. We find the exact value of the parking constant for this model.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"500 ","pages":"Article 129431"},"PeriodicalIF":3.5,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143724621","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}

{"title":"Sparse image representation through multiple multiresolution analysis","authors":"Mariantonia Cotronei ,&nbsp;Dörte Rüweler ,&nbsp;Tomas Sauer","doi":"10.1016/j.amc.2025.129440","DOIUrl":"10.1016/j.amc.2025.129440","url":null,"abstract":"<div><div>We present a strategy for image data sparsification based on a multiple multiresolution representation obtained through a structured tree of filterbanks, where both the filters and decimation matrices may vary with the decomposition level. As an extension of standard wavelet and wavelet-like approaches, our method also captures directional anisotropic information of the image while maintaining a controlled implementation complexity due to its filterbank structure and to the possibility of expressing the employed 2-D filters in an almost separable aspect. The focus of this work is on the transformation stage of image compression, emphasizing the sparsification of the transformed data. The proposed algorithm exploits the redundancy of the transformed image by applying an efficient sparse selection strategy, retaining a minimal yet representative subset of coefficients while preserving most of the energy of the data.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"500 ","pages":"Article 129440"},"PeriodicalIF":3.5,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143725611","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The reduction of block-transitive 3-(v,k,2) designs","authors":"Luozhong Gong ,&nbsp;Weijun Liu ,&nbsp;Shaojun Dai","doi":"10.1016/j.amc.2025.129435","DOIUrl":"10.1016/j.amc.2025.129435","url":null,"abstract":"<div><div>Using the O'Nan-Scott Theorem for classifying the primitive permutation group, the classification problem of 3-design is discussed. And the block-transitive and point-primitive automorphism groups of a 3-<span><math><mo>(</mo><mi>v</mi><mo>,</mo><mi>k</mi><mo>,</mo><mn>2</mn><mo>)</mo></math></span> designs is reduced to affine type and almost simple type.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"500 ","pages":"Article 129435"},"PeriodicalIF":3.5,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143724619","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}

{"title":"Maximal and maximum induced matchings in connected graphs","authors":"Bo-Jun Yuan ,&nbsp;Zhao-Yu Yang,&nbsp;Lu Zheng,&nbsp;Shi-Cai Gong","doi":"10.1016/j.amc.2025.129432","DOIUrl":"10.1016/j.amc.2025.129432","url":null,"abstract":"&lt;div&gt;&lt;div&gt;An induced matching is defined as a set of edges whose end-vertices induce a subgraph that is 1-regular. Building upon the work of Gupta et al. (2012) &lt;span&gt;&lt;span&gt;[11]&lt;/span&gt;&lt;/span&gt; and Basavaraju et al. (2016) &lt;span&gt;&lt;span&gt;[1]&lt;/span&gt;&lt;/span&gt;, who determined the maximum number of maximal induced matchings in general and triangle-free graphs respectively, this paper extends their findings to connected graphs with &lt;em&gt;n&lt;/em&gt; vertices. We establish a tight upper bound on the number of maximal and maximum induced matchings, as detailed below:&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mrow&gt;&lt;mi&gt;if&lt;/mi&gt;&lt;/mrow&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mn&gt;8&lt;/mn&gt;&lt;mo&gt;;&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mrow&gt;&lt;mo&gt;⌊&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;⌋&lt;/mo&gt;&lt;/mrow&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mrow&gt;&lt;mo&gt;⌈&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;⌉&lt;/mo&gt;&lt;/mrow&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;⌊&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;⌋&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;⌈&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;⌉&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mrow&gt;&lt;mi&gt;if&lt;/mi&gt;&lt;/mrow&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mn&gt;13&lt;/mn&gt;&lt;mo&gt;;&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mn&gt;10&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;144&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;30&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mrow&gt;&lt;mi&gt;if&lt;/mi&gt;&lt;/mrow&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mn&gt;14&lt;/mn&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mn&gt;30&lt;/mn&gt;&lt;mo&gt;;&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mn&gt;10&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mrow&gt;&lt;mi&gt;if&lt;/mi&gt;&lt;/mrow&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;31&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; This result not only provides a theoretical upper bound but also implies a practical algorithmic application: enumerating all maximal induced matchings of an &lt;em&gt;n&lt;/em&gt;-vertex connected graph in time &lt;span&gt;&lt;math&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"500 ","pages":"Article 129432"},"PeriodicalIF":3.5,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143705936","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}

{"title":"Graphs with span 1 and shortest optimal walks","authors":"Tanja Dravec ,&nbsp;Mirjana Mikalački ,&nbsp;Andrej Taranenko","doi":"10.1016/j.amc.2025.129433","DOIUrl":"10.1016/j.amc.2025.129433","url":null,"abstract":"<div><div>A span of a given graph <em>G</em> is the maximum distance that two players can keep at all times while visiting all vertices (edges) of <em>G</em> and moving according to certain rules, that produces different variants of span. We prove that the vertex and edge span of the same variant can differ by at most 1 and present a graph where the difference is exactly 1. For all variants of vertex span we present a lower bound in terms of the girth of the graph. Then we study graphs with the strong vertex span equal to 1. We present some nice properties of such graphs and show that interval graphs are contained in the class of graphs having the strong vertex span equal to 1. Finally, we present an algorithm that returns the minimum number of moves needed for both players to traverse all vertices of the given graph <em>G</em> such that in each move the distance between players equals at least the chosen vertex span of <em>G</em>.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"500 ","pages":"Article 129433"},"PeriodicalIF":3.5,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143724622","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}