Pub Date : 2023-07-30DOI: 10.29020/nybg.ejpam.v16i3.4766
Jahiri Manditong, Javier Hassan, Ladznar S. Laja, Amy A. Laja, N. H. M. Mohammad, Sisteta U. Kamdon
Let $G$ be a connected graph. A set $Dsubseteq V(G)$ is called a connected outer-hop independent dominating if $D$ is a connected dominating set and $V(G)s D$ is a hop independent set in $G$, respectively. The minimum cardinality of a connected outer-hop independent dominating set in $G$, denoted by $gamma_{c}^{ohi}(G)$, is called the connected outer-hop independent domination number of $G$. In this paper, we introduce and investigated the concept of connected outer-hop independent domination in a graph. We show that the connected outer-hop independent domination number and connected outer-independent domination number of a graph are incomparable. In fact, we find that their absolute difference can be made arbitrarily large. In addition, we characterize connected outer-hop independent dominating sets in graphs under some binary operations. Furthermore, these results are used to give exact values or bounds of the parameter for these graphs.
设$G$为连通图。如果$D$是连通控制集，$V(G) $ s $D$分别是$G$中的跳独立集，则集$D$称为连通外跳独立控制集。$G$中连通外跳独立支配集的最小基数，用$gamma_{c}^{ohi}(G)$表示，称为$G$的连通外跳独立支配数。本文引入并研究了图中连通外跳独立支配的概念。证明了图的连通外跳独立支配数和连通外跳独立支配数是不可比较的。事实上，我们发现它们的绝对差可以任意大。此外，我们还刻画了图在某些二元操作下的连通外跳独立支配集。此外，这些结果用于给出这些图的参数的精确值或边界。
{"title":"Connected Outer-Hop Independent Dominating Sets in Graphs Under Some Binary Operations","authors":"Jahiri Manditong, Javier Hassan, Ladznar S. Laja, Amy A. Laja, N. H. M. Mohammad, Sisteta U. Kamdon","doi":"10.29020/nybg.ejpam.v16i3.4766","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i3.4766","url":null,"abstract":"Let $G$ be a connected graph. A set $Dsubseteq V(G)$ is called a connected outer-hop independent dominating if $D$ is a connected dominating set and $V(G)s D$ is a hop independent set in $G$, respectively. The minimum cardinality of a connected outer-hop independent dominating set in $G$, denoted by $gamma_{c}^{ohi}(G)$, is called the connected outer-hop independent domination number of $G$. In this paper, we introduce and investigated the concept of connected outer-hop independent domination in a graph. We show that the connected outer-hop independent domination number and connected outer-independent domination number of a graph are incomparable. In fact, we find that their absolute difference can be made arbitrarily large. In addition, we characterize connected outer-hop independent dominating sets in graphs under some binary operations. Furthermore, these results are used to give exact values or bounds of the parameter for these graphs.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44820297","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 : 2023-07-30DOI: 10.29020/nybg.ejpam.v16i3.4810
C. J. Saromines, Sergio R. Canoy, Jr.
Let $G$ be an undirected graph with vertex and edge sets $V(G)$ and $E(G)$, respectively. A subset $S$ of vertices of $G$ is a geodetic hop dominating set if it is both a geodetic and a hop dominating set. The geodetic hop domination number of $G$ is the minimum cardinality among all geodetic hop dominating sets in $G$. Geodetic hop dominating sets in a graph resulting from the join of two graphs have been characterized. These characterizations have been used to determine the geodetic hop domination number of the graphs considered. A realization result involving the hop domination number and geodetic hop domination number is also obtained.
{"title":"Another Look at Geodetic Hop Domination in a Graph","authors":"C. J. Saromines, Sergio R. Canoy, Jr.","doi":"10.29020/nybg.ejpam.v16i3.4810","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i3.4810","url":null,"abstract":"Let $G$ be an undirected graph with vertex and edge sets $V(G)$ and $E(G)$, respectively. A subset $S$ of vertices of $G$ is a geodetic hop dominating set if it is both a geodetic and a hop dominating set. The geodetic hop domination number of $G$ is the minimum cardinality among all geodetic hop dominating sets in $G$. Geodetic hop dominating sets in a graph resulting from the join of two graphs have been characterized. These characterizations have been used to determine the geodetic hop domination number of the graphs considered. A realization result involving the hop domination number and geodetic hop domination number is also obtained.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45836315","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 : 2023-07-30DOI: 10.29020/nybg.ejpam.v16i3.4748
Miguel Varo Ortega, Gina A. Malacas, Sergio R. Canoy, Jr.
In this paper, we introduce and investigate the concept of global stable location-domination in graphs. We also characterize the global stable locating-dominating sets in the join, edge corona, corona, and lexicographic product of graphs and determine the exact value or sharp bound of the corresponding global stable location-domination number.
{"title":"Global Stable Location-Domination in Graphs","authors":"Miguel Varo Ortega, Gina A. Malacas, Sergio R. Canoy, Jr.","doi":"10.29020/nybg.ejpam.v16i3.4748","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i3.4748","url":null,"abstract":"In this paper, we introduce and investigate the concept of global stable location-domination in graphs. We also characterize the global stable locating-dominating sets in the join, edge corona, corona, and lexicographic product of graphs and determine the exact value or sharp bound of the corresponding global stable location-domination number.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45405120","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 : 2023-07-30DOI: 10.29020/nybg.ejpam.v16i3.4770
Angelica Mae Mahistrado, Helen M. Rara
Let $G$ be a connected graph. A set $S$ of vertices in $G$ is a 1-movable 2-resolving hop dominating set of $G$ if $S$ is a 2-resolving hop dominating set in $G$ and for every $v in S$, either $Sbackslash {v}$ is a 2-resolving hop dominating set of $G$ or there exists a vertex $u in big((V (G) backslash S) cap N_G(v)big)$ such that $big(S backslash {v}big) cup {u}$ is a 2-resolving hop dominating set of $G$. The 1-movable 2-resolving hop domination number of $G$, denoted by $gamma^{1}_{m2Rh}(G)$ is the smallest cardinality of a 1-movable 2-resolving hop dominating set of $G$. In this paper, we investigate the concept and study it for graphs resulting from some binary operations. Specifically, we characterize the 1-movable 2-resolving hop dominating sets in the join, corona and lexicographic products of graphs, and determine the bounds of the 1-movable 2-resolving hop domination number of each of these graphs.
{"title":"$1$-movable $2$-Resolving Hop Domination in Graph","authors":"Angelica Mae Mahistrado, Helen M. Rara","doi":"10.29020/nybg.ejpam.v16i3.4770","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i3.4770","url":null,"abstract":"Let $G$ be a connected graph. A set $S$ of vertices in $G$ is a 1-movable 2-resolving hop dominating set of $G$ if $S$ is a 2-resolving hop dominating set in $G$ and for every $v in S$, either $Sbackslash {v}$ is a 2-resolving hop dominating set of $G$ or there exists a vertex $u in big((V (G) backslash S) cap N_G(v)big)$ such that $big(S backslash {v}big) cup {u}$ is a 2-resolving hop dominating set of $G$. The 1-movable 2-resolving hop domination number of $G$, denoted by $gamma^{1}_{m2Rh}(G)$ is the smallest cardinality of a 1-movable 2-resolving hop dominating set of $G$. In this paper, we investigate the concept and study it for graphs resulting from some binary operations. Specifically, we characterize the 1-movable 2-resolving hop dominating sets in the join, corona and lexicographic products of graphs, and determine the bounds of the 1-movable 2-resolving hop domination number of each of these graphs.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46856108","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 : 2023-07-30DOI: 10.29020/nybg.ejpam.v16i3.4871
Ahmad Al Khalaf, I. Taha
Let G be a finite group. We say that G has the Basis Property if every subgroup H of G has a minimal generating set (basis), and any two bases of H have the same cardinality. A group G is called minimal not satisfying the Basis Property if it does not satisfy the Basis Property, but all its proper subgroups satisfy the Basis Property. We prove that the following groups PSL(2, 5) ∼A5, PSL(2, 8) , are minimal groups non satisfying the Basis Property, but the groups PSL(2, 9), PSL(2, 17) and PSL(3, 4) are not minimal and not satisfying the Basis Property.
{"title":"Finite Minimal Simple Groups Non-satisfying the Basis Property","authors":"Ahmad Al Khalaf, I. Taha","doi":"10.29020/nybg.ejpam.v16i3.4871","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i3.4871","url":null,"abstract":"Let G be a finite group. We say that G has the Basis Property if every subgroup H of G has a minimal generating set (basis), and any two bases of H have the same cardinality. A group G is called minimal not satisfying the Basis Property if it does not satisfy the Basis Property, but all its proper subgroups satisfy the Basis Property. We prove that the following groups PSL(2, 5) ∼A5, PSL(2, 8) , are minimal groups non satisfying the Basis Property, but the groups PSL(2, 9), PSL(2, 17) and PSL(3, 4) are not minimal and not satisfying the Basis Property.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43178466","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 : 2023-07-30DOI: 10.29020/nybg.ejpam.v16i3.4835
Nesba Nour El Houda, Beggas Mohammed, Belouafi Essaid, I. Ahmad, H. Ahmad, Sameh E Askar
In this research, we investigate the numerical solution of second member problems that depend on the solution obtained through a multigrid method. Specifically, we focus on the application of multigrid techniques for solving nonlinear variational inequalities. The main objective is to establish the uniform convergence of the multigrid algorithm. To achieve this, we employ elementary subdifferential calculus and draw insights from the convergence theory of nonlinear multigrid methods.
{"title":"Multigrid Methods for the Solution of Nonlinear Variational Inequalities","authors":"Nesba Nour El Houda, Beggas Mohammed, Belouafi Essaid, I. Ahmad, H. Ahmad, Sameh E Askar","doi":"10.29020/nybg.ejpam.v16i3.4835","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i3.4835","url":null,"abstract":"In this research, we investigate the numerical solution of second member problems that depend on the solution obtained through a multigrid method. Specifically, we focus on the application of multigrid techniques for solving nonlinear variational inequalities. The main objective is to establish the uniform convergence of the multigrid algorithm. To achieve this, we employ elementary subdifferential calculus and draw insights from the convergence theory of nonlinear multigrid methods.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46586137","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 : 2023-07-30DOI: 10.29020/nybg.ejpam.v16i3.4840
Sana Ullah Khan, Asif Khan, A. Ullah, Shabir Ahmad, Fuad A. Awwad, Emad A. A. Ismail, Shehu Maitama, Huzaifa Umar, H. Ahmad
Recently, Shehu has introduced an integral transform called Shehu transform, which generalizes the two well-known integrals transforms, i.e. Laplace and Sumudu transform. In the literature, many integral transforms were used to compute the solution of integro-differential equations (IDEs). In this article, for the first time, we use Shehu transform for the computation of solution of $n^{text{th}}$-order IDEs. We present a general scheme of solution for $n^{text{th}}$-order IDEs. We give some examples with detailed solutions to show the appropriateness of the method. We present the accuracy, simplicity, and convergence of the proposed method through tables and graphs.
{"title":"Solving nth-order Integro-differential Equations by Novel Generalized Hybrid Transform","authors":"Sana Ullah Khan, Asif Khan, A. Ullah, Shabir Ahmad, Fuad A. Awwad, Emad A. A. Ismail, Shehu Maitama, Huzaifa Umar, H. Ahmad","doi":"10.29020/nybg.ejpam.v16i3.4840","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i3.4840","url":null,"abstract":"Recently, Shehu has introduced an integral transform called Shehu transform, which generalizes the two well-known integrals transforms, i.e. Laplace and Sumudu transform. In the literature, many integral transforms were used to compute the solution of integro-differential equations (IDEs). In this article, for the first time, we use Shehu transform for the computation of solution of $n^{text{th}}$-order IDEs. We present a general scheme of solution for $n^{text{th}}$-order IDEs. We give some examples with detailed solutions to show the appropriateness of the method. We present the accuracy, simplicity, and convergence of the proposed method through tables and graphs.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41755330","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 : 2023-07-30DOI: 10.29020/nybg.ejpam.v16i3.4797
Renas T. M.Salim, N. Shuker
A ring R is considered a strongly 2-nil clean ring, or (strongly 2-NC ring for short), if each element in R can be expressed as the sum of a nilpotent and two idempotents that commute with each other. In this paper, further properties of strongly 2-NC rings are given. Furthermore, we introduce and explore a special type of strongly 2-NC ring where every unit is of order 2, which we refer to as a strongly 2-NC rings with U(R) = 2. It was proved that the Jacobson radical over a strongly 2-NC ring is a nil ideal, here, we demonstrated that the Jacobson radical over strongly 2-NC ring with U(R) = 2 is a nil ideal of characteristic 4. We compare this ring with other rings, since every SNC ring is strongly 2-NC, but not every unit of order 2, and if R is a strongly 2-NC with U(R) = 2, then R need not be SNC ring. In order to get N il(R) = 0, we added one more condition involving this ring.
{"title":"Strongly 2-Nil Clean Rings with Units of Order Two","authors":"Renas T. M.Salim, N. Shuker","doi":"10.29020/nybg.ejpam.v16i3.4797","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i3.4797","url":null,"abstract":"A ring R is considered a strongly 2-nil clean ring, or (strongly 2-NC ring for short), if each element in R can be expressed as the sum of a nilpotent and two idempotents that commute with each other. In this paper, further properties of strongly 2-NC rings are given. Furthermore, we introduce and explore a special type of strongly 2-NC ring where every unit is of order 2, which we refer to as a strongly 2-NC rings with U(R) = 2. It was proved that the Jacobson radical over a strongly 2-NC ring is a nil ideal, here, we demonstrated that the Jacobson radical over strongly 2-NC ring with U(R) = 2 is a nil ideal of characteristic 4. We compare this ring with other rings, since every SNC ring is strongly 2-NC, but not every unit of order 2, and if R is a strongly 2-NC with U(R) = 2, then R need not be SNC ring. In order to get N il(R) = 0, we added one more condition involving this ring.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47239406","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 : 2023-07-30DOI: 10.29020/nybg.ejpam.v16i3.4722
Farwa Asmat, Humaira Asmat, Sameh E Askar, H. Ahmad, Muhammad Ijaz Khan
It was introduced by Doˇsli ́c and Ivica et al. (Journal of Mathematical chemistry, 56(10) (2018): 2995–3013), as an innovative graph-theoretic topological identifier, the Mostar index is significant in simulating compounds’ thermodynamic properties in simulations, which is defined as sum of absolute values of the differences among nu(e|Ω) and nv(e|Ω) over all lines e = uv ∈ Ω, where nu(e|Ω) (resp. nv(e|Ω)) is the collection of vertices of Ω closer to vertex u (resp. v) than to vertex v (resp. u). Let C(n, k) be the set of all n-vertex cacti graphs with exactly k cycles and T(n, d) be the set of all n-vertex tree graphs with diameter d. It is said that a cacti is a connected graph with blocks that comprise of either cycles or edges. Beginning with the weighted Mostar index of graphs, we developed certain transformations that either increase or decrease index. To advance this analysis, we determine the extreme graphs where the maximum and minimum values of the weighted edge Mostar index are accomplished. Moreover, we compute the maximum weighted vertex Mostar invariant for trees with order n and fixed diameter d.
{"title":"On Weighted Vertex and Edge Mostar Index for Trees and Cacti with Fixed Parameter","authors":"Farwa Asmat, Humaira Asmat, Sameh E Askar, H. Ahmad, Muhammad Ijaz Khan","doi":"10.29020/nybg.ejpam.v16i3.4722","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i3.4722","url":null,"abstract":"It was introduced by Doˇsli ́c and Ivica et al. (Journal of Mathematical chemistry, 56(10) (2018): 2995–3013), as an innovative graph-theoretic topological identifier, the Mostar index is significant in simulating compounds’ thermodynamic properties in simulations, which is defined as sum of absolute values of the differences among nu(e|Ω) and nv(e|Ω) over all lines e = uv ∈ Ω, where nu(e|Ω) (resp. nv(e|Ω)) is the collection of vertices of Ω closer to vertex u (resp. v) than to vertex v (resp. u). Let C(n, k) be the set of all n-vertex cacti graphs with exactly k cycles and T(n, d) be the set of all n-vertex tree graphs with diameter d. It is said that a cacti is a connected graph with blocks that comprise of either cycles or edges. Beginning with the weighted Mostar index of graphs, we developed certain transformations that either increase or decrease index. To advance this analysis, we determine the extreme graphs where the maximum and minimum values of the weighted edge Mostar index are accomplished. Moreover, we compute the maximum weighted vertex Mostar invariant for trees with order n and fixed diameter d.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44851535","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 : 2023-07-30DOI: 10.29020/nybg.ejpam.v16i3.4808
Ahlam Ahmed Alharbi, A. Kılıçman
This article's main aim is to study the concepts of the generalized neighborhood and generalized quasi-neighborhood in fuzzy bitopological spaces. It also introduces fundamental theorems for determining the relationships between them. Additionally, some significant examples were examined to demonstrate the significance of the interconnections, some theorems were also introduced to study some main properties of neighborhood structures. Finally, we also studied the concepts of closure, interior, and each of their critical theories and properties by generalized neighborhood systems in fuzzy bitopological spaces.
{"title":"Note on Generalized Neighborhoods Structures in Fuzzy Bitopological Spaces","authors":"Ahlam Ahmed Alharbi, A. Kılıçman","doi":"10.29020/nybg.ejpam.v16i3.4808","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i3.4808","url":null,"abstract":"This article's main aim is to study the concepts of the generalized neighborhood and generalized quasi-neighborhood in fuzzy bitopological spaces. It also introduces fundamental theorems for determining the relationships between them. Additionally, some significant examples were examined to demonstrate the significance of the interconnections, some theorems were also introduced to study some main properties of neighborhood structures. Finally, we also studied the concepts of closure, interior, and each of their critical theories and properties by generalized neighborhood systems in fuzzy bitopological spaces.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47265667","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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