Let R be a ring with unity. Taloukolaei and Sahebi [2] introduced the Von Neumann regular graph G... more Let R be a ring with unity. Taloukolaei and Sahebi [2] introduced the Von Neumann regular graph GV nr+(R) of a ring, whose vertex set is R and two distinct vertices x and y are adjacent if and only if x + y is a Von Neumann regular element. In this article, we investigate some new properties of GV nr+(R) such as traversability, pancyclic, unicyclic, chordal and perfect. We also investigate the domination parameters of GV nr+(R) such as dominating set, domination number, total domination number, connected domination number and give the condition when the GV nr+(R) is an excellent graph. Finally we determine the bondage number.
Let R be a ring with unity. Taloukolaei and Sahebi [2] introduced the Von Neumann regular graph G... more Let R be a ring with unity. Taloukolaei and Sahebi [2] introduced the Von Neumann regular graph GV nr+(R) of a ring, whose vertex set is R and two distinct vertices x and y are adjacent if and only if x + y is a Von Neumann regular element. In this article, we investigate some new properties of GV nr+(R) such as traversability, pancyclic, unicyclic, chordal and perfect. We also investigate the domination parameters of GV nr+(R) such as dominating set, domination number, total domination number, connected domination number and give the condition when the GV nr+(R) is an excellent graph. Finally we determine the bondage number.
In this paper, we prove that the closure formula for ideals in C(X) under m topology holds in int... more In this paper, we prove that the closure formula for ideals in C(X) under m topology holds in intermediate ring also, i.e. for any ideal I in an intermediate ring with m topology, its closure is the intersection of all the maximal ideals containing I.
In this paper, we introduce the double total graph of a finite commutative ring R with non-zero u... more In this paper, we introduce the double total graph of a finite commutative ring R with non-zero unity, denoted by
In this paper properties of super-continuous are further studied. In addition, two new separation... more In this paper properties of super-continuous are further studied. In addition, two new separation axioms for a topological space viz. feebly-regular space and completely feebly-regular spaces are introduced and their basic properties are studied. Keywords super-closed; super-open; super-continuity; feebly-regular; completely feebly-regular
Journal of Information and Optimization Sciences, 2017
In this paper, we study some graphs associated to a finite dimensional vector space V over a fini... more In this paper, we study some graphs associated to a finite dimensional vector space V over a finite field. We characterize vector spaces such that the associated graph is Hamiltonian and Eulerian. We also characterize vector spaces for which the associate graphs are planar and toroidal and also we find the independence number and domination number of some graphs.
Communications in Mathematics and Applications, 2021
Considering a commutative ring \(R\) with unity as the set of vertices and two vertices \(x\) and... more Considering a commutative ring \(R\) with unity as the set of vertices and two vertices \(x\) and \(y\) are adjacent if and only if \(u+(x+y) \in Z(R)\) for some \(u \in U(R)\), the resulting graph \(T_{u}(\Gamma(R))\) is known as the double total graph . In this paper we find the degree of any vertex in \(T_{u}(\Gamma(R))\) for a weakly unit fusible ring \(R\) and domination number of \(T_{u}(\Gamma(R))\) for any ring \(R\). Also, we investigate the properties of \(T_{u}(\Gamma(\mathbb{Z}_{n}\times\mathbb{Z}_{m}))\) and characterize $R$ in terms of toroidal \(T_{u}(\Gamma(R))\).
The annihilator graph $AG(R)$ of a commutative ring $R$ is a simple undirected graph with the ve... more The annihilator graph $AG(R)$ of a commutative ring $R$ is a simple undirected graph with the vertex set $Z(R)^*$ and two distinct vertices are adjacent if and only if $ann(x) cup ann(y)$ $ neq $ $ann(xy)$. In this paper we give the sufficient condition for a graph $AG(R)$ to be complete. We characterize rings for which $AG(R)$ is a regular graph, we show that $gamma (AG(R))in {1,2}$ and we also characterize the rings for which $AG(R)$ has a cut vertex. Finally we find the clique number of a finite reduced ring and characterize the rings for which $AG(R)$ is a planar graph.
Let R be a ring with unity. Taloukolaei and Sahebi [2] introduced the Von Neumann regular graph G... more Let R be a ring with unity. Taloukolaei and Sahebi [2] introduced the Von Neumann regular graph GV nr+(R) of a ring, whose vertex set is R and two distinct vertices x and y are adjacent if and only if x + y is a Von Neumann regular element. In this article, we investigate some new properties of GV nr+(R) such as traversability, pancyclic, unicyclic, chordal and perfect. We also investigate the domination parameters of GV nr+(R) such as dominating set, domination number, total domination number, connected domination number and give the condition when the GV nr+(R) is an excellent graph. Finally we determine the bondage number.
Let R be a ring with unity. Taloukolaei and Sahebi [2] introduced the Von Neumann regular graph G... more Let R be a ring with unity. Taloukolaei and Sahebi [2] introduced the Von Neumann regular graph GV nr+(R) of a ring, whose vertex set is R and two distinct vertices x and y are adjacent if and only if x + y is a Von Neumann regular element. In this article, we investigate some new properties of GV nr+(R) such as traversability, pancyclic, unicyclic, chordal and perfect. We also investigate the domination parameters of GV nr+(R) such as dominating set, domination number, total domination number, connected domination number and give the condition when the GV nr+(R) is an excellent graph. Finally we determine the bondage number.
In this paper, we prove that the closure formula for ideals in C(X) under m topology holds in int... more In this paper, we prove that the closure formula for ideals in C(X) under m topology holds in intermediate ring also, i.e. for any ideal I in an intermediate ring with m topology, its closure is the intersection of all the maximal ideals containing I.
In this paper, we introduce the double total graph of a finite commutative ring R with non-zero u... more In this paper, we introduce the double total graph of a finite commutative ring R with non-zero unity, denoted by
In this paper properties of super-continuous are further studied. In addition, two new separation... more In this paper properties of super-continuous are further studied. In addition, two new separation axioms for a topological space viz. feebly-regular space and completely feebly-regular spaces are introduced and their basic properties are studied. Keywords super-closed; super-open; super-continuity; feebly-regular; completely feebly-regular
Journal of Information and Optimization Sciences, 2017
In this paper, we study some graphs associated to a finite dimensional vector space V over a fini... more In this paper, we study some graphs associated to a finite dimensional vector space V over a finite field. We characterize vector spaces such that the associated graph is Hamiltonian and Eulerian. We also characterize vector spaces for which the associate graphs are planar and toroidal and also we find the independence number and domination number of some graphs.
Communications in Mathematics and Applications, 2021
Considering a commutative ring \(R\) with unity as the set of vertices and two vertices \(x\) and... more Considering a commutative ring \(R\) with unity as the set of vertices and two vertices \(x\) and \(y\) are adjacent if and only if \(u+(x+y) \in Z(R)\) for some \(u \in U(R)\), the resulting graph \(T_{u}(\Gamma(R))\) is known as the double total graph . In this paper we find the degree of any vertex in \(T_{u}(\Gamma(R))\) for a weakly unit fusible ring \(R\) and domination number of \(T_{u}(\Gamma(R))\) for any ring \(R\). Also, we investigate the properties of \(T_{u}(\Gamma(\mathbb{Z}_{n}\times\mathbb{Z}_{m}))\) and characterize $R$ in terms of toroidal \(T_{u}(\Gamma(R))\).
The annihilator graph $AG(R)$ of a commutative ring $R$ is a simple undirected graph with the ve... more The annihilator graph $AG(R)$ of a commutative ring $R$ is a simple undirected graph with the vertex set $Z(R)^*$ and two distinct vertices are adjacent if and only if $ann(x) cup ann(y)$ $ neq $ $ann(xy)$. In this paper we give the sufficient condition for a graph $AG(R)$ to be complete. We characterize rings for which $AG(R)$ is a regular graph, we show that $gamma (AG(R))in {1,2}$ and we also characterize the rings for which $AG(R)$ has a cut vertex. Finally we find the clique number of a finite reduced ring and characterize the rings for which $AG(R)$ is a planar graph.
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Papers by Sanghita Dutta