{"title":"The Metric Dimension of Subdivisions of Lilly Graph, Tadpole Graph and Special Trees","authors":"Basma Mohamed, Mohamed Amin","doi":"10.11648/j.acm.20231201.12","DOIUrl":"https://doi.org/10.11648/j.acm.20231201.12","url":null,"abstract":": Consider a robot that is navigating in a space represented by a graph and wants to know its current location. It can send a signal to find out how far it is from each set of fixed landmarks. We study the problem of computing the minimum number of landmarks required, and where they should be placed so that the robot can always determine its location. The set of nodes where the landmarks are located is called the metric basis of the graph, and the number of landmarks is called the metric dimension of the graph. On the other hand, the metric dimension of a graph G is the smallest size of a set B of vertices that can distinguish each vertex pair of G by the shortest-path distance to some vertex in B . The finding of the metric dimension of an arbitrary graph is an NP-complete problem. Also, the metric dimension has several applications in different areas, such as geographical routing protocols, network discovery and verification, pattern recognition, image processing, and combinatorial optimization. In this paper, we study the metric dimension of subdivisions of several graphs, including the Lilly graph, the Tadpole graph, and the special trees star tree, bistar tree, and coconut tree.","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":"20 1","pages":""},"PeriodicalIF":10.0,"publicationDate":"2023-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89058111","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":"An Integrable Nonlinear Wave Model: Darboux Transform and Exact Solutions","authors":"Jingru Geng, Minna Feng","doi":"10.11648/j.acm.20231201.11","DOIUrl":"https://doi.org/10.11648/j.acm.20231201.11","url":null,"abstract":": Soliton equations are infinite-dimensional integrable systems described by nonlinear partial differential equations. In the mathematical theory of soliton equations, the discovery of integrability of these equations has greatly promoted the understanding of their generality","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":"12 1","pages":""},"PeriodicalIF":10.0,"publicationDate":"2023-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88713624","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":"Analysis of an extended gene regulatory network model with time delay","authors":"","doi":"10.30546/1683-6154.22.2.2023.225","DOIUrl":"https://doi.org/10.30546/1683-6154.22.2.2023.225","url":null,"abstract":"","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":"308 1","pages":""},"PeriodicalIF":10.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77216341","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":"Detection of resistance spot welding faults in copper materials by transfer learning method","authors":"","doi":"10.30546/1683-6154.22.3.2023.430","DOIUrl":"https://doi.org/10.30546/1683-6154.22.3.2023.430","url":null,"abstract":"","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":"32 1","pages":""},"PeriodicalIF":10.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87116859","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":"A novel approach on high order Runge-Kutta-Nyström error estimators","authors":"","doi":"10.30546/1683-6154.22.2.2023.246","DOIUrl":"https://doi.org/10.30546/1683-6154.22.2.2023.246","url":null,"abstract":"","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":"57 1","pages":""},"PeriodicalIF":10.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84540061","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":"Effective trajectories of economic dynamics models on graphs","authors":"","doi":"10.30546/1683-6154.22.2.2023.215","DOIUrl":"https://doi.org/10.30546/1683-6154.22.2.2023.215","url":null,"abstract":"","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":"65 1","pages":""},"PeriodicalIF":10.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73745363","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":"Dynamics of a periodic stage-structure competitive model with two maturation delays","authors":"","doi":"10.30546/1683-6154.22.2.2023.149","DOIUrl":"https://doi.org/10.30546/1683-6154.22.2.2023.149","url":null,"abstract":"","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":"82 13","pages":""},"PeriodicalIF":10.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72485082","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":"Novel generalizations for Grüss type inequalities pertaining to the constant proportional fractional integrals","authors":"","doi":"10.30546/1683-6154.22.2.2023.275","DOIUrl":"https://doi.org/10.30546/1683-6154.22.2.2023.275","url":null,"abstract":"","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":"39 1","pages":""},"PeriodicalIF":10.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76591238","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":"Deep learning driven smart education: teaching management mechanism based on metaverse and big data analysis","authors":"","doi":"10.30546/1683-6154.22.3.2023.355","DOIUrl":"https://doi.org/10.30546/1683-6154.22.3.2023.355","url":null,"abstract":"","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":"103 1","pages":""},"PeriodicalIF":10.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77918480","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":"An Analytical Study of Fractional Delay Impulsive Implicit Systems with Mittag-Leffler Law","authors":"","doi":"10.30546/1683-6154.22.1.2023.31","DOIUrl":"https://doi.org/10.30546/1683-6154.22.1.2023.31","url":null,"abstract":"","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":"67 1","pages":""},"PeriodicalIF":10.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72874655","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}