Pub Date : 2024-03-16DOI: 10.1142/s1793830924500034
Roman Kolpakov
In this paper, we consider a tree-like recursion procedure of solving of binary decomposable problems. More specifically, we study some questions of parallelization of this procedure with using of shared round memory. We consider two parallelization schemes for parallel solving of binary decomposable problems by tree-like recursion procedures on a parallel computing system with shared round memory. We call these schemes the TAN-scheme and the TON-scheme of parallelization. We compare the efficiency of these schemes, using different parameters of parallelization. Based on this comparative analysis, we conclude the TON-scheme to be more effective.
在本文中，我们考虑了求解二元可分解问题的树状递归过程。更具体地说，我们研究了利用共享轮内存并行化这一过程的一些问题。我们考虑了在具有共享轮内存的并行计算系统上通过树状递归程序并行求解二元可分解问题的两种并行化方案。我们将这两种并行化方案分别称为 TAN 方案和 TON 方案。我们使用不同的并行化参数来比较这些方案的效率。根据比较分析，我们认为 TON 方案更为有效。
{"title":"The comparing analysis of two parallelization schemes for computations with round memory","authors":"Roman Kolpakov","doi":"10.1142/s1793830924500034","DOIUrl":"https://doi.org/10.1142/s1793830924500034","url":null,"abstract":"In this paper, we consider a tree-like recursion procedure of solving of binary decomposable problems. More specifically, we study some questions of parallelization of this procedure with using of shared round memory. We consider two parallelization schemes for parallel solving of binary decomposable problems by tree-like recursion procedures on a parallel computing system with shared round memory. We call these schemes the TAN-scheme and the TON-scheme of parallelization. We compare the efficiency of these schemes, using different parameters of parallelization. Based on this comparative analysis, we conclude the TON-scheme to be more effective.","PeriodicalId":504044,"journal":{"name":"Discrete Mathematics, Algorithms and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140237207","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-13DOI: 10.1142/s1793830924500289
Vahid Nourozi, Farhad Rahmati
{"title":"The Rank of the Cartier Operator on Picard Curves","authors":"Vahid Nourozi, Farhad Rahmati","doi":"10.1142/s1793830924500289","DOIUrl":"https://doi.org/10.1142/s1793830924500289","url":null,"abstract":"","PeriodicalId":504044,"journal":{"name":"Discrete Mathematics, Algorithms and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140247056","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-23DOI: 10.1142/s1793830924500198
Mohamed Abd Allah El-Hadidy
{"title":"Discrete Search Stability for a Hidden target on M-intervals with a Known Probabilistic Distributed Effort","authors":"Mohamed Abd Allah El-Hadidy","doi":"10.1142/s1793830924500198","DOIUrl":"https://doi.org/10.1142/s1793830924500198","url":null,"abstract":"","PeriodicalId":504044,"journal":{"name":"Discrete Mathematics, Algorithms and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140435565","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-23DOI: 10.1142/s1793830924500204
Usman Babar, Asim Naseem, Hani Shaker, Muhammad Kamran Siddiqui, Muhammad Faisal Nadeem
{"title":"On Physical Analysis of Eccentricity Based Topological Indices for Hex Derived Networks","authors":"Usman Babar, Asim Naseem, Hani Shaker, Muhammad Kamran Siddiqui, Muhammad Faisal Nadeem","doi":"10.1142/s1793830924500204","DOIUrl":"https://doi.org/10.1142/s1793830924500204","url":null,"abstract":"","PeriodicalId":504044,"journal":{"name":"Discrete Mathematics, Algorithms and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140436566","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-23DOI: 10.1142/s1793830924500186
Emad Kareem Mutar
{"title":"Estimating the reliability bounds of communication system by using Sum of Disjoint product Method","authors":"Emad Kareem Mutar","doi":"10.1142/s1793830924500186","DOIUrl":"https://doi.org/10.1142/s1793830924500186","url":null,"abstract":"","PeriodicalId":504044,"journal":{"name":"Discrete Mathematics, Algorithms and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140438076","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-16DOI: 10.1142/s1793830924500058
S. Niazian, M. Aaly Kologani, R. A. Borzooei
In this paper, we introduced the notion of hyper [Formula: see text]-algebras as a generalization of [Formula: see text]-algebras. We studied basic properties of them and investigated the relationship among hyper [Formula: see text]-algebras and some other hyper logical algebras such as hyper ([Formula: see text],BCI) BCK-algebras and hyper hoops. In the following, we defined the notions of (weak) hyper ideals in hyper [Formula: see text]-algebras and then by considering the congruence relation (relative to a hyper ideal) on the hyper [Formula: see text]-algebra, we constructed the quotient hyper [Formula: see text]-algebras and investigated some properties of them.
{"title":"Hyper L-algebras","authors":"S. Niazian, M. Aaly Kologani, R. A. Borzooei","doi":"10.1142/s1793830924500058","DOIUrl":"https://doi.org/10.1142/s1793830924500058","url":null,"abstract":"In this paper, we introduced the notion of hyper [Formula: see text]-algebras as a generalization of [Formula: see text]-algebras. We studied basic properties of them and investigated the relationship among hyper [Formula: see text]-algebras and some other hyper logical algebras such as hyper ([Formula: see text],BCI) BCK-algebras and hyper hoops. In the following, we defined the notions of (weak) hyper ideals in hyper [Formula: see text]-algebras and then by considering the congruence relation (relative to a hyper ideal) on the hyper [Formula: see text]-algebra, we constructed the quotient hyper [Formula: see text]-algebras and investigated some properties of them.","PeriodicalId":504044,"journal":{"name":"Discrete Mathematics, Algorithms and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140454541","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-14DOI: 10.1142/s1793830924500071
A. Rao, Sandeep Kumar, Deepa Sinha
Let [Formula: see text] be the ring of integer modulo [Formula: see text] with two binary operators, addition [Formula: see text] and multiplication [Formula: see text], where [Formula: see text] is a positive integer. The special set [Formula: see text] is defined as [Formula: see text]. Our purpose in the present paper is to propose a new family of interconnection networks that are Cayley graphs on this special set [Formula: see text] and denote it by [Formula: see text]. In this paper, we define a relationship between [Formula: see text] and [Formula: see text], [Formula: see text] is a derived graph from [Formula: see text] by removing [Formula: see text] edges, where [Formula: see text] is a known fixed value. We also give the spectrum of absorption Cayley graph, unitary addition Cayley graph, and [Formula: see text]. We also provide values of [Formula: see text] for which the graph [Formula: see text] is hyperenergetic and discuss the structural properties of this graph, such as planarity and connectedness.
{"title":"Spectral analysis of a graph on the special set 𝒮","authors":"A. Rao, Sandeep Kumar, Deepa Sinha","doi":"10.1142/s1793830924500071","DOIUrl":"https://doi.org/10.1142/s1793830924500071","url":null,"abstract":"Let [Formula: see text] be the ring of integer modulo [Formula: see text] with two binary operators, addition [Formula: see text] and multiplication [Formula: see text], where [Formula: see text] is a positive integer. The special set [Formula: see text] is defined as [Formula: see text]. Our purpose in the present paper is to propose a new family of interconnection networks that are Cayley graphs on this special set [Formula: see text] and denote it by [Formula: see text]. In this paper, we define a relationship between [Formula: see text] and [Formula: see text], [Formula: see text] is a derived graph from [Formula: see text] by removing [Formula: see text] edges, where [Formula: see text] is a known fixed value. We also give the spectrum of absorption Cayley graph, unitary addition Cayley graph, and [Formula: see text]. We also provide values of [Formula: see text] for which the graph [Formula: see text] is hyperenergetic and discuss the structural properties of this graph, such as planarity and connectedness.","PeriodicalId":504044,"journal":{"name":"Discrete Mathematics, Algorithms and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139836746","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-14DOI: 10.1142/s1793830924500071
A. Rao, Sandeep Kumar, Deepa Sinha
Let [Formula: see text] be the ring of integer modulo [Formula: see text] with two binary operators, addition [Formula: see text] and multiplication [Formula: see text], where [Formula: see text] is a positive integer. The special set [Formula: see text] is defined as [Formula: see text]. Our purpose in the present paper is to propose a new family of interconnection networks that are Cayley graphs on this special set [Formula: see text] and denote it by [Formula: see text]. In this paper, we define a relationship between [Formula: see text] and [Formula: see text], [Formula: see text] is a derived graph from [Formula: see text] by removing [Formula: see text] edges, where [Formula: see text] is a known fixed value. We also give the spectrum of absorption Cayley graph, unitary addition Cayley graph, and [Formula: see text]. We also provide values of [Formula: see text] for which the graph [Formula: see text] is hyperenergetic and discuss the structural properties of this graph, such as planarity and connectedness.
{"title":"Spectral analysis of a graph on the special set 𝒮","authors":"A. Rao, Sandeep Kumar, Deepa Sinha","doi":"10.1142/s1793830924500071","DOIUrl":"https://doi.org/10.1142/s1793830924500071","url":null,"abstract":"Let [Formula: see text] be the ring of integer modulo [Formula: see text] with two binary operators, addition [Formula: see text] and multiplication [Formula: see text], where [Formula: see text] is a positive integer. The special set [Formula: see text] is defined as [Formula: see text]. Our purpose in the present paper is to propose a new family of interconnection networks that are Cayley graphs on this special set [Formula: see text] and denote it by [Formula: see text]. In this paper, we define a relationship between [Formula: see text] and [Formula: see text], [Formula: see text] is a derived graph from [Formula: see text] by removing [Formula: see text] edges, where [Formula: see text] is a known fixed value. We also give the spectrum of absorption Cayley graph, unitary addition Cayley graph, and [Formula: see text]. We also provide values of [Formula: see text] for which the graph [Formula: see text] is hyperenergetic and discuss the structural properties of this graph, such as planarity and connectedness.","PeriodicalId":504044,"journal":{"name":"Discrete Mathematics, Algorithms and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139777235","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-14DOI: 10.1142/s179383092450006x
Hao Zhou, Maqsood Ahmad, Muhammad Kamran Siddiqui
Graph operations play a significant role in constructing new and valuable graphs and capturing intermolecular forces between atoms and bonds of a molecule. In mathematical chemistry and chemical graph theory, a topological invariant is a numeric value extracted from the molecular graph of a chemical compound using a mathematical formula involving vertex degrees, distance, spectrum, and their combination. An intriguing problem in chemical graph theory is figuring out the lower and the upper bound on pertinent topological indices among a particular family of graphs. The first Gourava index for a graph [Formula: see text] is denoted and defined as [Formula: see text] Recently, Kulli studied and derived formulas of the first Gourava index for four graph operations. We proved with the help of counter-examples that the results provided by Kulli produce inaccurate values when compared with exact values. In this paper, we determined the exact formulas and bounds of the first Gourava index for [Formula: see text]-sum graphs. Besides, we presented diverse examples to support our results.
{"title":"On some bounds of first Gourava index for Ψ-sum graphs","authors":"Hao Zhou, Maqsood Ahmad, Muhammad Kamran Siddiqui","doi":"10.1142/s179383092450006x","DOIUrl":"https://doi.org/10.1142/s179383092450006x","url":null,"abstract":"Graph operations play a significant role in constructing new and valuable graphs and capturing intermolecular forces between atoms and bonds of a molecule. In mathematical chemistry and chemical graph theory, a topological invariant is a numeric value extracted from the molecular graph of a chemical compound using a mathematical formula involving vertex degrees, distance, spectrum, and their combination. An intriguing problem in chemical graph theory is figuring out the lower and the upper bound on pertinent topological indices among a particular family of graphs. The first Gourava index for a graph [Formula: see text] is denoted and defined as [Formula: see text] Recently, Kulli studied and derived formulas of the first Gourava index for four graph operations. We proved with the help of counter-examples that the results provided by Kulli produce inaccurate values when compared with exact values. In this paper, we determined the exact formulas and bounds of the first Gourava index for [Formula: see text]-sum graphs. Besides, we presented diverse examples to support our results.","PeriodicalId":504044,"journal":{"name":"Discrete Mathematics, Algorithms and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139839349","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-14DOI: 10.1142/s179383092450006x
Hao Zhou, Maqsood Ahmad, Muhammad Kamran Siddiqui
Graph operations play a significant role in constructing new and valuable graphs and capturing intermolecular forces between atoms and bonds of a molecule. In mathematical chemistry and chemical graph theory, a topological invariant is a numeric value extracted from the molecular graph of a chemical compound using a mathematical formula involving vertex degrees, distance, spectrum, and their combination. An intriguing problem in chemical graph theory is figuring out the lower and the upper bound on pertinent topological indices among a particular family of graphs. The first Gourava index for a graph [Formula: see text] is denoted and defined as [Formula: see text] Recently, Kulli studied and derived formulas of the first Gourava index for four graph operations. We proved with the help of counter-examples that the results provided by Kulli produce inaccurate values when compared with exact values. In this paper, we determined the exact formulas and bounds of the first Gourava index for [Formula: see text]-sum graphs. Besides, we presented diverse examples to support our results.
{"title":"On some bounds of first Gourava index for Ψ-sum graphs","authors":"Hao Zhou, Maqsood Ahmad, Muhammad Kamran Siddiqui","doi":"10.1142/s179383092450006x","DOIUrl":"https://doi.org/10.1142/s179383092450006x","url":null,"abstract":"Graph operations play a significant role in constructing new and valuable graphs and capturing intermolecular forces between atoms and bonds of a molecule. In mathematical chemistry and chemical graph theory, a topological invariant is a numeric value extracted from the molecular graph of a chemical compound using a mathematical formula involving vertex degrees, distance, spectrum, and their combination. An intriguing problem in chemical graph theory is figuring out the lower and the upper bound on pertinent topological indices among a particular family of graphs. The first Gourava index for a graph [Formula: see text] is denoted and defined as [Formula: see text] Recently, Kulli studied and derived formulas of the first Gourava index for four graph operations. We proved with the help of counter-examples that the results provided by Kulli produce inaccurate values when compared with exact values. In this paper, we determined the exact formulas and bounds of the first Gourava index for [Formula: see text]-sum graphs. Besides, we presented diverse examples to support our results.","PeriodicalId":504044,"journal":{"name":"Discrete Mathematics, Algorithms and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139779590","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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