Pub Date : 2024-01-31DOI: 10.29020/nybg.ejpam.v17i1.4973
Alhousseynou Ba, M. A. Diompy, A. S. Diabang
Let R be an associative ring and M a unitary left R-module. An R-module M is said to be uniserial if its submodules are linearly ordered by inclusion. A serial module is a direct sum of uniserial modules. In this paper, we bring our modest contribution to the open problem listed in the book of Alberto Facchini "Module Theory" which states that is any direct summand of a serial module serial? The answer is yes for particular rings and R-modules.
假设 R 是一个关联环，M 是一个单元左 R 模块。如果 R 模块 M 的子模块通过包含线性有序，则称其为单列模块。序列模块是单列模块的直接和。阿尔贝托-法奇尼在《模块理论》一书中提出了一个悬而未决的问题：序列模块的任何直接和都是序列的吗？对于特定的环和 R 模块，答案是肯定的。
{"title":"Direct Summand of Serial Modules","authors":"Alhousseynou Ba, M. A. Diompy, A. S. Diabang","doi":"10.29020/nybg.ejpam.v17i1.4973","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v17i1.4973","url":null,"abstract":"Let R be an associative ring and M a unitary left R-module. An R-module M is said to be uniserial if its submodules are linearly ordered by inclusion. A serial module is a direct sum of uniserial modules. In this paper, we bring our modest contribution to the open problem listed in the book of Alberto Facchini \"Module Theory\" which states that is any direct summand of a serial module serial? The answer is yes for particular rings and R-modules. ","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140474251","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 : 2024-01-31DOI: 10.29020/nybg.ejpam.v17i1.5024
Faizah Alharbi, Sharifah Althubiti
In this article, the Volterra-Fredholm integral equation (V-FIE) is derived from an initial value problem of kind integro-differential equation (IVP). We discuss the existence and uniqueness of the solution to the problem in Hilbert space. A numerical method is used to reduce this type of equation to System of Fredholm integral equations of the second kind(SFIEs). In light of this, the clustering method and the Galerkin method to solve the system of second-order Fredholm integral equations(SFIEs) and calculate the error in each case. Finally, the approximate and exact solutions are plotted on the same coordinate plane Using MATLAB code (2022).
{"title":"Numerical Simulation of Initial Value Problem of Integro-differential Equation Models","authors":"Faizah Alharbi, Sharifah Althubiti","doi":"10.29020/nybg.ejpam.v17i1.5024","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v17i1.5024","url":null,"abstract":"In this article, the Volterra-Fredholm integral equation (V-FIE) is derived from an initial value problem of kind integro-differential equation (IVP). We discuss the existence and uniqueness of the solution to the problem in Hilbert space. A numerical method is used to reduce this type of equation to System of Fredholm integral equations of the second kind(SFIEs). In light of this, the clustering method and the Galerkin method to solve the system of second-order Fredholm integral equations(SFIEs) and calculate the error in each case. Finally, the approximate and exact solutions are plotted on the same coordinate plane Using MATLAB code (2022).","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140472231","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 : 2024-01-31DOI: 10.29020/nybg.ejpam.v17i1.5051
Rizalyn Bongcawel, Lyster Rey Cabardo, Gaudencio C. Petalcorin, Jr., Jocelyn Vilela
This study introduces an ample Hausdorff groupoid $hat{A} rtimes mathcal{R}$ extracted from an ample Hausdorff groupoid $mathcal{G}$ and a unital commutative ring $R$; a Hausdorff groupoid $D$ which is the discrete twist over $hat{A} rtimes mathcal{R}$. In the groupoid C*-algebra perspective, when $R = mathbb{C}$ there is an isomorphism between the non-twisted groupoid C*-algebra $(C^*(mathcal{G}))$ and the twisted groupoid C*-algebra $(C^*(hat{A} rtimes mathcal{R};D))$. However, in this paper, in a purely algebraic setting, the non-twisted Steinberg algebra $(A_R(mathcal{G}))$ and the twisted Steinberg algebra $(A_R(D; hat{A} rtimes mathcal{R}))$ are non-isomorphic.
{"title":"On the Construction of a Groupoid from an Ample Hausdorff Groupoid with Twisted Steinberg Algebra not Isomorphic to its Non-twisted Steinberg Algebra","authors":"Rizalyn Bongcawel, Lyster Rey Cabardo, Gaudencio C. Petalcorin, Jr., Jocelyn Vilela","doi":"10.29020/nybg.ejpam.v17i1.5051","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v17i1.5051","url":null,"abstract":"This study introduces an ample Hausdorff groupoid $hat{A} rtimes mathcal{R}$ extracted from an ample Hausdorff groupoid $mathcal{G}$ and a unital commutative ring $R$; a Hausdorff groupoid $D$ which is the discrete twist over $hat{A} rtimes mathcal{R}$. In the groupoid C*-algebra perspective, when $R = mathbb{C}$ there is an isomorphism between the non-twisted groupoid C*-algebra $(C^*(mathcal{G}))$ and the twisted groupoid C*-algebra $(C^*(hat{A} rtimes mathcal{R};D))$. However, in this paper, in a purely algebraic setting, the non-twisted Steinberg algebra $(A_R(mathcal{G}))$ and the twisted Steinberg algebra $(A_R(D; hat{A} rtimes mathcal{R}))$ are non-isomorphic.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140475230","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 : 2024-01-31DOI: 10.29020/nybg.ejpam.v17i1.5015
I. Nawajah, H. Kanj, Y. Kotb, Julian Hoxha, Mouhammad Alakkoumi, Kamel Jebreen
Bayesian estimation of the linear regression parameter system is considered by deploying Median Rank Set Sampling (MRSS). The full conditional distributions and the associated posterior distribution are obtained. Therefore, based on Markov Chain Monte Carlo simulation, the Bayesian point estimates and credible intervals for the regression parameters are determined. To measure the efficiency of the obtained Bayesian estimates concerning the frequentist estimates we compute the asymptotic relative efficiency of the obtained Bayesian estimates using Markov Chain Monte Carlo simulation.
{"title":"Bayesian Regression Analysis using Median Rank Set Sampling","authors":"I. Nawajah, H. Kanj, Y. Kotb, Julian Hoxha, Mouhammad Alakkoumi, Kamel Jebreen","doi":"10.29020/nybg.ejpam.v17i1.5015","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v17i1.5015","url":null,"abstract":"Bayesian estimation of the linear regression parameter system is considered by deploying Median Rank Set Sampling (MRSS). The full conditional distributions and the associated posterior distribution are obtained. Therefore, based on Markov Chain Monte Carlo simulation, the Bayesian point estimates and credible intervals for the regression parameters are determined. To measure the efficiency of the obtained Bayesian estimates concerning the frequentist estimates we compute the asymptotic relative efficiency of the obtained Bayesian estimates using Markov Chain Monte Carlo simulation.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140476790","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 : 2024-01-31DOI: 10.29020/nybg.ejpam.v17i1.4987
Adama Kiemtore, W. O. Sawadogo, Fatima Aquel, Hamza Alaa, K. S. Somda
Hepatitis is a viral infection that can cause inflammation of the liver and lead to severe liver damage and even death. The study of hepatitis in Burkina Faso is crucial for several reasons. Indeed, understanding the epidemiology of hepatitis in Burkina Faso can help develop effective prevention and control strategies, and its study can contribute to a better understanding of the global burden of the disease and the development of effective interventions in other parts of the world. To this aim, a new differential susceptibility and infectivity mathematical model of Hepatitis B transmission was developed in order to simulate the potential spread of the Hepatitis B virus in the population of Burkina Faso. Once the mathematical model is presented, the existence and uniqueness of non-negative solutions are proved. The model has a globally asymptotically stable disease-free equilibrium when the basic reproduction number R01 and a globally asymptotically stable endemic equilibrium when R0 > 1. The global asymptotic stability of the disease-free equilibrium has been studied using the Castillo Chavez method [5]. The Lyapunov function and the LaSalle invariance principle are used to prove the global asymptotic stability of the endemic equilibrium [26, 4, 18]. To simulate the proposed model, a Matlab numerical code has been developed. Numerical simulations are performed using data of Burkina Faso. The obtained numerical results confirm analytical results as well as the evolution of hepatitis B in Burkina Faso.
{"title":"Mathematical Modelling and Numerical Simulation of Hepatitis B Viral Infection: The Case of Burkina Faso","authors":"Adama Kiemtore, W. O. Sawadogo, Fatima Aquel, Hamza Alaa, K. S. Somda","doi":"10.29020/nybg.ejpam.v17i1.4987","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v17i1.4987","url":null,"abstract":"Hepatitis is a viral infection that can cause inflammation of the liver and lead to severe liver damage and even death. The study of hepatitis in Burkina Faso is crucial for several reasons. Indeed, understanding the epidemiology of hepatitis in Burkina Faso can help develop effective prevention and control strategies, and its study can contribute to a better understanding of the global burden of the disease and the development of effective interventions in other parts of the world. To this aim, a new differential susceptibility and infectivity mathematical model of Hepatitis B transmission was developed in order to simulate the potential spread of the Hepatitis B virus in the population of Burkina Faso. Once the mathematical model is presented, the existence and uniqueness of non-negative solutions are proved. The model has a globally asymptotically stable disease-free equilibrium when the basic reproduction number R01 and a globally asymptotically stable endemic equilibrium when R0 > 1. The global asymptotic stability of the disease-free equilibrium has been studied using the Castillo Chavez method [5]. The Lyapunov function and the LaSalle invariance principle are used to prove the global asymptotic stability of the endemic equilibrium [26, 4, 18]. To simulate the proposed model, a Matlab numerical code has been developed. Numerical simulations are performed using data of Burkina Faso. The obtained numerical results confirm analytical results as well as the evolution of hepatitis B in Burkina Faso.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140476525","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 : 2024-01-31DOI: 10.29020/nybg.ejpam.v17i1.4979
Michael P. May
We apply the Inclusion-Exclusion Principle to a unique pair of prime number subsequences to determine whether these subsequences form a small set or a large set and thus whether the infinite sum of the inverse of their terms converges or diverges. In this paper, we analyze the complementary prime number subsequences P′ and P′′ as well as revisit the twin prime subsequence P2.
{"title":"Application of the Inclusion-Exclusion Principle to Prime Number Subsequences","authors":"Michael P. May","doi":"10.29020/nybg.ejpam.v17i1.4979","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v17i1.4979","url":null,"abstract":"We apply the Inclusion-Exclusion Principle to a unique pair of prime number subsequences to determine whether these subsequences form a small set or a large set and thus whether the infinite sum of the inverse of their terms converges or diverges. In this paper, we analyze the complementary prime number subsequences P′ and P′′ as well as revisit the twin prime subsequence P2.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140479637","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 : 2024-01-31DOI: 10.29020/nybg.ejpam.v17i1.5008
M. Alshayea
This paper focuses on exploring restricted mathematical concepts within the domain of BCK/BCI-algebras, specifically delving into the intricate realm of Multi-polar Q-hesitant fuzzy soft implicative and positive implicative ideals. BCK and BCI-algebras are pivotal structures in mathematical logic and algebraic systems, finding widespread applications in fields like computer science and artificial intelligence. Our contribution lies in the introduction and thorough investigation of the innovative notions of multi-polar Q-hesitant fuzzy soft implicative and positive implicative ideals, uniquely tailored for BCK/BCI-algebras. These ideals exhibit exceptional flexibility in managing uncertain and hesitant information, serving as potent tools for modeling and solvingreal-world problems characterized by imprecise or incomplete data. This study rigorously defines and explores the foundational properties of multi-polar Q-hesitant fuzzy soft implicative ideals, underscoring their relevance and applicability within BCK/BCI-algebras. Additionally, we present the concept of positive implicative ideals, establishing their interconnectedness with multi-polar Q-hesitant fuzzy soft implicative ideals. Our investigation delves into these ideals’ algebraic and logical facets, offering valuable insights into their mutual interactions and significance within the context of BCK/BCI-algebras. To facilitate practical implementation, we develop algorithms and methodologies for identifying and characterizing multi-polar Q-hesitant fuzzy soft implicative and positive implicative ideals. These computational tools enable efficient decision-making in scenariosinvolving uncertainty. Through illustrative examples and case studies, we showcase the potential of these ideals in handling complex, uncertain information, demonstrating their efficacy in aiding problem-solving processes. This research contributes significantly to advancing BCK/BCI-algebra theory by introducing innovative mathematical structures that bridge the gap between fuzzy logic, soft computing, and implicative ideals. The proposed multi-polar Q-hesitant fuzzy soft implicativeand positive implicative ideals open new avenues for addressing real-world problems characterized by imprecision and uncertainty. As such, they represent a valuable addition to the field of algebraic structures and their applications.
{"title":"Multi-polar Q-hesitant Fuzzy Soft Implicative and Positive Implicative Ideals in BCK/BCI-algebras.","authors":"M. Alshayea","doi":"10.29020/nybg.ejpam.v17i1.5008","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v17i1.5008","url":null,"abstract":"This paper focuses on exploring restricted mathematical concepts within the domain of BCK/BCI-algebras, specifically delving into the intricate realm of Multi-polar Q-hesitant fuzzy soft implicative and positive implicative ideals. BCK and BCI-algebras are pivotal structures in mathematical logic and algebraic systems, finding widespread applications in fields like computer science and artificial intelligence. Our contribution lies in the introduction and thorough investigation of the innovative notions of multi-polar Q-hesitant fuzzy soft implicative and positive implicative ideals, uniquely tailored for BCK/BCI-algebras. These ideals exhibit exceptional flexibility in managing uncertain and hesitant information, serving as potent tools for modeling and solvingreal-world problems characterized by imprecise or incomplete data. This study rigorously defines and explores the foundational properties of multi-polar Q-hesitant fuzzy soft implicative ideals, underscoring their relevance and applicability within BCK/BCI-algebras. Additionally, we present the concept of positive implicative ideals, establishing their interconnectedness with multi-polar Q-hesitant fuzzy soft implicative ideals. Our investigation delves into these ideals’ algebraic and logical facets, offering valuable insights into their mutual interactions and significance within the context of BCK/BCI-algebras. To facilitate practical implementation, we develop algorithms and methodologies for identifying and characterizing multi-polar Q-hesitant fuzzy soft implicative and positive implicative ideals. These computational tools enable efficient decision-making in scenariosinvolving uncertainty. Through illustrative examples and case studies, we showcase the potential of these ideals in handling complex, uncertain information, demonstrating their efficacy in aiding problem-solving processes. This research contributes significantly to advancing BCK/BCI-algebra theory by introducing innovative mathematical structures that bridge the gap between fuzzy logic, soft computing, and implicative ideals. The proposed multi-polar Q-hesitant fuzzy soft implicativeand positive implicative ideals open new avenues for addressing real-world problems characterized by imprecision and uncertainty. As such, they represent a valuable addition to the field of algebraic structures and their applications.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140474525","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 : 2024-01-31DOI: 10.29020/nybg.ejpam.v17i1.4978
Vergel Bilar, Maria Andrea O. Bonsocan, Javier A. Hassan, Susan C. Dagondon
Let $G$ be a graph. Then a subset $C$ of vertices of $G$ is called a vertex cover hop dominating if $C$ is both a vertex cover and a hop dominating of $G$. The vertex cover hop domination number of $G$, denoted by $gamma_{vch}(G)$, is the minimum cardinality among all vertex cover hop dominating sets in $G$. In this paper, we initiate the study of vertex cover hop domination in a graph and we determine its relations with other parameters in graph theory. We characterize the vertex cover hop dominating sets in some special graphs, join, and corona of two graphs and we finally obtain the exact values or bounds of the parameters of these graphs.
{"title":"Vertex Cover Hop Dominating Sets in Graphs","authors":"Vergel Bilar, Maria Andrea O. Bonsocan, Javier A. Hassan, Susan C. Dagondon","doi":"10.29020/nybg.ejpam.v17i1.4978","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v17i1.4978","url":null,"abstract":"Let $G$ be a graph. Then a subset $C$ of vertices of $G$ is called a vertex cover hop dominating if $C$ is both a vertex cover and a hop dominating of $G$. The vertex cover hop domination number of $G$, denoted by $gamma_{vch}(G)$, is the minimum cardinality among all vertex cover hop dominating sets in $G$. In this paper, we initiate the study of vertex cover hop domination in a graph and we determine its relations with other parameters in graph theory. We characterize the vertex cover hop dominating sets in some special graphs, join, and corona of two graphs and we finally obtain the exact values or bounds of the parameters of these graphs.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140475115","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 : 2024-01-31DOI: 10.29020/nybg.ejpam.v17i1.4983
Somphong Jitman, Pornrudee Modjam
Arrowhead matrices have attracted attention due to their rich algebraic structures and numerous applications. In this paper, we focus on the enumeration of n × n arrowhead matrices with prescribed determinant over a finite field Fq and over a finite commutative chain ring R. The number of n × n arrowhead matrices over Fq of a fixed determinant a is determined for all positiveintegers n and for all elements a ∈ Fq. As applications, this result is used in the enumeration of n × n non-singular arrowhead matrices with prescribed determinant over R. Subsequently, some bounds on the number of n × n singular arrowhead matrices over R of a fixed determinant are given. Finally, some open problems are presented.
箭头矩阵因其丰富的代数结构和众多应用而备受关注。对于所有正整数 n 和所有元素 a∈Fq 来说，固定行列式 a 的 n × n 箭头矩阵的数目是确定的。作为应用，这一结果被用于枚举 R 上具有规定行列式的 n × n 非奇异镞矩阵。随后，给出了关于 R 上具有固定行列式的 n × n 奇异镞矩阵数量的一些界限。最后，提出了一些悬而未决的问题。
{"title":"Determinants of Arrowhead Matrices over Finite Commutative Chain Rings","authors":"Somphong Jitman, Pornrudee Modjam","doi":"10.29020/nybg.ejpam.v17i1.4983","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v17i1.4983","url":null,"abstract":"Arrowhead matrices have attracted attention due to their rich algebraic structures and numerous applications. In this paper, we focus on the enumeration of n × n arrowhead matrices with prescribed determinant over a finite field Fq and over a finite commutative chain ring R. The number of n × n arrowhead matrices over Fq of a fixed determinant a is determined for all positiveintegers n and for all elements a ∈ Fq. As applications, this result is used in the enumeration of n × n non-singular arrowhead matrices with prescribed determinant over R. Subsequently, some bounds on the number of n × n singular arrowhead matrices over R of a fixed determinant are given. Finally, some open problems are presented.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140476262","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 : 2024-01-31DOI: 10.29020/nybg.ejpam.v17i1.5019
Sakthidevi Kaliyaperumal, Kalyani Desikan
Consider G a simple connected graph. In this paper, we introduce the Universal distance matrix UD (G). For α, β, γ, δ ∈ R and β ̸= 0, the universal distance matrix UD (G) is defined asUD (G) = αTr (G) + βD(G) + γJ + δI,where Tr (G) is the diagonal matrix whose elements are the vertex transmissions, and D(G) is the distance matrix of G. Here J is the all-ones matrix, and I is the identity matrix. In this paper, we obtain the universal distance spectra of regular graph, join of two regular graphs, joined union of three regular graphs, generalized joined union of n disjoint graphs with one arbitrary graph H. As a consequence, we obtain the eigenvalues of distance matrix, distance Laplacian matrix, distance signless Laplacian matrix, generalized distance matrix, distance Seidal matrix and distance matrices of complementary graphs.
考虑 G 是一个简单的连通图。本文引入通用距离矩阵 UD (G)。对于 α, β, γ, δ∈ R 且 β̸= 0，通用距离矩阵 UD (G) 定义为UD (G) = αTr (G) + βD(G) + γJ + δI，其中 Tr (G) 是对角矩阵，其元素为顶点传递，D(G) 是 G 的距离矩阵。因此，我们得到了互补图的距离矩阵、距离拉普拉斯矩阵、距离无符号拉普拉斯矩阵、广义距离矩阵、距离塞达矩阵和距离矩阵的特征值。
{"title":"Universal Distance Spectra of Join of Graphs","authors":"Sakthidevi Kaliyaperumal, Kalyani Desikan","doi":"10.29020/nybg.ejpam.v17i1.5019","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v17i1.5019","url":null,"abstract":"Consider G a simple connected graph. In this paper, we introduce the Universal distance matrix UD (G). For α, β, γ, δ ∈ R and β ̸= 0, the universal distance matrix UD (G) is defined asUD (G) = αTr (G) + βD(G) + γJ + δI,where Tr (G) is the diagonal matrix whose elements are the vertex transmissions, and D(G) is the distance matrix of G. Here J is the all-ones matrix, and I is the identity matrix. In this paper, we obtain the universal distance spectra of regular graph, join of two regular graphs, joined union of three regular graphs, generalized joined union of n disjoint graphs with one arbitrary graph H. As a consequence, we obtain the eigenvalues of distance matrix, distance Laplacian matrix, distance signless Laplacian matrix, generalized distance matrix, distance Seidal matrix and distance matrices of complementary graphs.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140478090","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：