Tamizh Chelvam T
Manonmaniam Sundaranar University, Mathematics, Faculty Member
Research Interests:
Let R be a commutative ring with identity and let Nil(R) be the ideal of all 2 nilpotent elements of R. Let I(R) = {I : I is a non-trivial ideal of R and there exists a 3 non-trivial ideal J such that IJ ⊆ Nil(R)}. The nil-graph of ideals... more
Let R be a commutative ring with identity and let Nil(R) be the ideal of all 2 nilpotent elements of R. Let I(R) = {I : I is a non-trivial ideal of R and there exists a 3 non-trivial ideal J such that IJ ⊆ Nil(R)}. The nil-graph of ideals of R is defined as the 4 simple undirected graph AG N (R) whose vertex set is I(R) and two distinct vertices I and 5 J are adjacent if and only if IJ ⊆ Nil(R). In this paper, we study the planarity and genus of 6 AG N (R). In particular, we have characterized all commutative Artin rings R for which the 7 genus of AG N (R) is either zero or one.
Let R be a commutative ring with identity and let Nil(R) be the ideal of all 2 nilpotent elements of R. Let I(R) = {I : I is a non-trivial ideal of R and there exists a 3 non-trivial ideal J such that IJ ⊆ Nil(R)}. The nil-graph of ideals... more
Let R be a commutative ring with identity and let Nil(R) be the ideal of all 2 nilpotent elements of R. Let I(R) = {I : I is a non-trivial ideal of R and there exists a 3 non-trivial ideal J such that IJ ⊆ Nil(R)}. The nil-graph of ideals of R is defined as the 4 simple undirected graph AG N (R) whose vertex set is I(R) and two distinct vertices I and 5 J are adjacent if and only if IJ ⊆ Nil(R). In this paper, we study the planarity and genus of 6 AG N (R). In particular, we have characterized all commutative Artin rings R for which the 7 genus of AG N (R) is either zero or one.
Research Interests:
Research Interests:
Let R be a commutative ring with identity and A * (R) the set of non-zero ideals with non-zero annihilators. The annihilating-ideal graph of R is defined as the graph AG(R) with the vertex set A * (R) and two distinct vertices I 1 and I 2... more
Let R be a commutative ring with identity and A * (R) the set of non-zero ideals with non-zero annihilators. The annihilating-ideal graph of R is defined as the graph AG(R) with the vertex set A * (R) and two distinct vertices I 1 and I 2 are adjacent if and only if I 1 I 2 = (0). In this paper, we examine the presence of cut vertices and cut sets in the annihilating-ideal graph of a commutative Artinian ring and provide a partial classification of the rings in which they appear. Using this, we obtain the vertex connectivity of some annihilating-ideal graphs.
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The directed zero-divisor graph is a graph constructed out of a non-commutative ring R and its non-zero zero-divisors Z(R) *. The zero-divisor graph Γ(R) of a non-commutative ring R is a directed graph with vertex set Z(R) * , where for... more
The directed zero-divisor graph is a graph constructed out of a non-commutative ring R and its non-zero zero-divisors Z(R) *. The zero-divisor graph Γ(R) of a non-commutative ring R is a directed graph with vertex set Z(R) * , where for distinct vertices x and y of Z(R) * there is a directed edge from x to y if and only if xy = 0 in R. In this paper, we attempt to find the various domination parameters for the directed zero-divisor graph constructed out of M 2 (Z p), where p is a prime number.
Research Interests:
In this paper, we study about the intersection graph of gamma sets in the zero-divisor graph of the commutative ring Z n. The intersection graph of gamma sets is a graph with vertex set as the collection of all gamma sets of the... more
In this paper, we study about the intersection graph of gamma sets in the zero-divisor graph of the commutative ring Z n. The intersection graph of gamma sets is a graph with vertex set as the collection of all gamma sets of the zero-divisor graph of Z n and two distinct vertices A and B are adjacent if and only if A ∩ B ̸ = ∅. This graph is denoted by I Γ (Z n). We investigate the interplay between the graph theoretic properties of I Γ (Z n) and the ring theoretic properties of Z n and we attempt to find the various domination parameters for the intersection graph of gamma sets in the zero-divisor graph of Z n .
Research Interests:
Research Interests:
Abstract. In this paper, we obtain necessary and sufficient conditions for the existence of an efficient dominating set in the Cartesian product of two cycles and in the Cartesian product of three cycles. When $2 n+ 1$ is prime and $ k_i... more
Abstract. In this paper, we obtain necessary and sufficient conditions for the existence of an efficient dominating set in the Cartesian product of two cycles and in the Cartesian product of three cycles. When $2 n+ 1$ is prime and $ k_i $'s are multiples of $2 n+ 1$, we obtain all efficient dominating sets in the Cartesian product of $ n $ cycles $\ square _ {i= 1}^{n} C_ {k_i} $.
Abstract. We introduce the concept of a morphism between fuzzy sets, which enables us to define the category of fuzzy sets. Next, we give elementwise characterization of some special morphisms in this category which will be useful for... more
Abstract. We introduce the concept of a morphism between fuzzy sets, which enables us to define the category of fuzzy sets. Next, we give elementwise characterization of some special morphisms in this category which will be useful for later studies. We prove that unlike the category of sets, this category is not balanced. Also, we prove that this category has equalizers, coequalizers, intersections, images and weak inverse images.
Addendum to “A result concerning the stability of some difference equations and its applications” by Hark-Mahn Kim, Vol. 112, No. 3, pp. 453–462 ............. ... Generalized (m, n) bi-ideals of a near-ring... more
Addendum to “A result concerning the stability of some difference equations and its applications” by Hark-Mahn Kim, Vol. 112, No. 3, pp. 453–462 ............. ... Generalized (m, n) bi-ideals of a near-ring ................................... ....................................... T Tamizh Chelvam and S Jayalakshmi 479 ... Limits of rank 4 Azumaya algebras and applications to desingularization........ ............... ..........................................TE Venkata Balaji 485 ... A general theorem characterizing some absolute summability methods ......... .............................................................WT Sulaiman 543
Research Interests:
Research Interests:
Efficient open dominating sets in bipartite Cayley graphs are characterized in terms of covering projections. Necessary and sufficient conditions for the existence of efficient open dominating sets in certain circulant Harary graphs are... more
Efficient open dominating sets in bipartite Cayley graphs are characterized in terms of covering projections. Necessary and sufficient conditions for the existence of efficient open dominating sets in certain circulant Harary graphs are given. Chains of efficient dominating sets, and of efficient open dominating sets, in families of circulant graphs are described as an application.
Research Interests:
Abstract. In this paper, we obtain necessary and sufficient conditions for the existence of an efficient dominating set in the Cartesian product of two cycles and in the Cartesian product of three cycles. When $2 n+ 1$ is prime and $ k_i... more
Abstract. In this paper, we obtain necessary and sufficient conditions for the existence of an efficient dominating set in the Cartesian product of two cycles and in the Cartesian product of three cycles. When $2 n+ 1$ is prime and $ k_i $'s are multiples of $2 n+ 1$, we obtain all efficient dominating sets in the Cartesian product of $ n $ cycles $\ square _ {i= 1}^{n} C_ {k_i} $.
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Let R be a commutative ring. The intersection graph of gamma sets in the zero-divisor graph Γ(R) of R is the graph IΓ(R) with vertex set as the collection of all gamma sets of the zero-divisor graph Γ(R) of R and two distinct vertices A... more
Let R be a commutative ring. The intersection graph of gamma sets in the zero-divisor
graph Γ(R) of R is the graph IΓ(R) with vertex set as the collection of all gamma sets
of the zero-divisor graph Γ(R) of R and two distinct vertices A and B are adjacent if
and only if A ∩ B = ∅. In this paper, we study about various properties of IΓ(R) and
investigate the interplay between the graph theoretic properties of IΓ(R) and the ring
theoretic properties of R.
graph Γ(R) of R is the graph IΓ(R) with vertex set as the collection of all gamma sets
of the zero-divisor graph Γ(R) of R and two distinct vertices A and B are adjacent if
and only if A ∩ B = ∅. In this paper, we study about various properties of IΓ(R) and
investigate the interplay between the graph theoretic properties of IΓ(R) and the ring
theoretic properties of R.
Research Interests:
Let G be a group. The power graph P (G) of G is a graph with vertex set V (P (G)) = G and two distinct vertices x and y are adjacent in P (G) if and only if either xi = y or yj = x, where 2 ≤ i, j ≤ n. In this paper, we obtain some... more
Let G be a group. The power graph P (G) of G
is a graph with vertex set V (P (G)) = G and two distinct vertices x and y are adjacent in P (G) if and only if either xi = y or yj = x, where 2 ≤ i, j ≤ n. In this paper, we obtain some fundamental characterizations of the power graph. Also, we characterize certain classes of power graphs of finite abelian groups.
is a graph with vertex set V (P (G)) = G and two distinct vertices x and y are adjacent in P (G) if and only if either xi = y or yj = x, where 2 ≤ i, j ≤ n. In this paper, we obtain some fundamental characterizations of the power graph. Also, we characterize certain classes of power graphs of finite abelian groups.
Research Interests:
In this paper, we study the notion of ideal based zero divisor graph structure of gamma near- ring M with respect to
reflexive ideal I of M.
reflexive ideal I of M.
Research Interests:
Research Interests:
Abstract A near-ring N is said to be S1 if for every a∈ N, there exists x∈ N∗= N−{0} such that axa= xa. Closely following this, we introduce in this paper the concept of S2 near-rings. A near-ring N is said to be an S2 near-ring if, for... more
Abstract A near-ring N is said to be S1 if for every a∈ N, there exists x∈ N∗= N−{0} such that axa= xa. Closely following this, we introduce in this paper the concept of S2 near-rings. A near-ring N is said to be an S2 near-ring if, for every a∈ N, there exists x∈ N∗ such that axa= ax. Further by generalizing this, we introduce strong S2 near-rings ie, near-rings in which aba= ab for all a, b∈ N. We discuss some of their properties, obtain a characterisation and also a structure theorem. Keywords S2 near-rings, strong S2 near-rings, zero divisors.
Abstract In [3] we defined a right near ring (N,+,·) to be an S1-near ring if for every a∈ N, there exists x∈ N∗, where N∗= N-{0}, such that axa= xa. In this paper we call N a Strong S1-near ring if for every a∈ N,{x∈ N∗| axa= xa}= N∗. We... more
Abstract In [3] we defined a right near ring (N,+,·) to be an S1-near ring if for every a∈ N, there exists x∈ N∗, where N∗= N-{0}, such that axa= xa. In this paper we call N a Strong S1-near ring if for every a∈ N,{x∈ N∗| axa= xa}= N∗. We study some of its important properties, obtain a characterization and also a structure theorem under certain conditions.
Abstract A near-ring N is called weak commutative (Definition 9.4, p. 289, Pilz [7]) if xyz= xzy for every x, y, z∈ N. It is quite natural to investigate the properties of N if xyz= zyx for every x, y, z∈ N. We call such a near-ring a... more
Abstract A near-ring N is called weak commutative (Definition 9.4, p. 289, Pilz [7]) if xyz= xzy for every x, y, z∈ N. It is quite natural to investigate the properties of N if xyz= zyx for every x, y, z∈ N. We call such a near-ring a pseudo commutative nearring. In this paper, we furnish examples of such near-rings and probe certain properties of pseudo commutative near-rings. We also discuss the properties of pseudo commutative nearring which are regular. We obtain some equivalent conditions for a near-ring to be pseudo commutative.
Abstract In this paper we introduce the concepts of B1 near-rings and strong B1 near-rings. We say that a right near-ring N is a B1 near-ring if for every a∈ N, there exists x∈ N∗ where N∗= N−{0}, such that Nax= Nxa. By the way of... more
Abstract In this paper we introduce the concepts of B1 near-rings and strong B1 near-rings. We say that a right near-ring N is a B1 near-ring if for every a∈ N, there exists x∈ N∗ where N∗= N−{0}, such that Nax= Nxa. By the way of generalization, we define N as a strong B1 near-ring if Nab= Nba for all a, b∈ N. We discuss some of their properties, obtain a characterisation and also a structure theorem.
Page 1. BULLETIN OF INTERNATIONAL MATHEMATICAL VIRTUAL INSTITUTE ISSN 1840-4367 Vol. 2(2012), 9-16 Former BULLETIN OF SOCIETY OF MATHEMATICIANS BANJA LUKA ISSN 0354-5792 (o), ISSN 1986-521X (p) STRONGLY REGULAR INTEGRAL CIRCULANT GRAPHS... more
Page 1. BULLETIN OF INTERNATIONAL MATHEMATICAL VIRTUAL INSTITUTE ISSN 1840-4367 Vol. 2(2012), 9-16 Former BULLETIN OF SOCIETY OF MATHEMATICIANS BANJA LUKA ISSN 0354-5792 (o), ISSN 1986-521X (p) STRONGLY REGULAR INTEGRAL CIRCULANT GRAPHS AND THEIR ENERGIES Thirugnanam Tamizh Chelvam1, Sekar Raja2 and Ivan Gutman3 Abstract. Let S ⊂ Zn be a finite cyclic group of order n 李 1.
ABSTRACT The'Gestation period'or the infecundable period of pregnancy measured from the date of conception to the date of termination of pregnancy by live birth, is a useful item for consideration in certain biological and public health... more
ABSTRACT The'Gestation period'or the infecundable period of pregnancy measured from the date of conception to the date of termination of pregnancy by live birth, is a useful item for consideration in certain biological and public health problems, Bartholomew (1973) has analyzed some of Markov chain model. In this paper, the equilibrium state of the human gestation period for mature and premature babies, the biological character of the mothers from the hospital data are analyzed.
Abstract Cayley graphs are graphs constructed out of a finite group Γ and its generating set A. Let G be a group and let H be a subgroup of G. The Cayley graph (G, G− H) is called the Subgroup Complementary Cayley graph and it is denoted... more
Abstract Cayley graphs are graphs constructed out of a finite group Γ and its generating set A. Let G be a group and let H be a subgroup of G. The Cayley graph (G, G− H) is called the Subgroup Complementary Cayley graph and it is denoted by SC (G, H). In this paper, some graph theoretical properties of SC (G, H) are obtained and through which the structure of such graphs are analyzed.
Abstract A set ${S\ subseteq V} $ is said to be a complementary nil dominating set of a graph $ G $ if it is a dominating set and its complement ${VS} $ is not a dominating set for $ G $. The minimum cardinality of a $ cnd $-set is called... more
Abstract A set ${S\ subseteq V} $ is said to be a complementary nil dominating set of a graph $ G $ if it is a dominating set and its complement ${VS} $ is not a dominating set for $ G $. The minimum cardinality of a $ cnd $-set is called the complementary nil domination number of $ G $ and is denoted by ${\ gamma} _ {\ rm cnd}(G) $. In this paper some results on the complementary nil domination number are obtained.
Abstract: A Cayley graph is constructed out of a group Γ and its generating set X and it is denoted by С (Γ, X). A Smarandachely n-Cayley graph is defined to be G= ZC (Γ, X), where V (G)= Γ× Zn and E (G)={((x, 0),(y, 1)) a,((x, 1),(y, 2))... more
Abstract: A Cayley graph is constructed out of a group Γ and its generating set X and it is denoted by С (Γ, X). A Smarandachely n-Cayley graph is defined to be G= ZC (Γ, X), where V (G)= Γ× Zn and E (G)={((x, 0),(y, 1)) a,((x, 1),(y, 2)) a,···,((x, n− 2),(y, n− 1)) a: x, y∈ Γ, a∈ X such that y= x∗ a}. Particularly, a Smarandachely 2-Cayley graph is called as a Bi-Cayley graph, denoted by BС (Γ, X).
Abstract: A circulant graph is a Cayley graph constructed out of a finite cyclic group Γ and a generating set A is a subset of Γ. In this paper, we attempt to find upper bounds for distance-g domination, distance-g paired domination and... more
Abstract: A circulant graph is a Cayley graph constructed out of a finite cyclic group Γ and a generating set A is a subset of Γ. In this paper, we attempt to find upper bounds for distance-g domination, distance-g paired domination and distance-g connected domination number for circulant graphs. Exact values are also determined in certain cases. Key Words: Circulant graph, Smarandachely distance-g paired-(U, V) dominating P-set, distance-g domination, distance-g paired, total and connected domination, distance-g efficient domination.
ABSTRACT In this paper, sharp upper bounds for the domination number, total domination number and connected domination number for the Cayley graph G= Cay (D2n, Ω) constructed on the finite dihedral group D2n, and a specified generating... more
ABSTRACT In this paper, sharp upper bounds for the domination number, total domination number and connected domination number for the Cayley graph G= Cay (D2n, Ω) constructed on the finite dihedral group D2n, and a specified generating set Ω of D2n. Further efficient dominating sets in G= Cay (D2n, Ω) are also obtained. More specifically, it is proved that some of the proper subgroups of D2n are efficient domination sets. Using this, an E-chain of Cayley graphs on the dihedral group is also constructed.