Volume 4 (2016) Article in Press

ISSUE 1 − A ISSUE 1 − B ISSUE 1 − C ISSUE 1 − D
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Article Type : Research Article
Title : Complementary Tree Domination in Unicyclic Graphs
Country : India
Authors : S.Muthammai || P.Vidhya

Abstract: A set $D$ of a graph $G = (V, E)$ is a dominating set of every vertex in $V-D$ is adjacent to some vertex in $D$. The domination number $\gamma(G)$ of $G$ is the minimum cardinality of a dominating set. A dominating set $D$ is called a complementary tree dominating set if the induced subgraph $$ is a tree. The minimum cardinality of a complementary tree dominating set is called the complementary tree domination number of $G$ and is denoted by $\gamma_{ctd}(G)$. In this paper, connected unicyclic graphs for which $\gamma_{ctd}(G) = \gamma(G)$ nad $\gamma_{ctd}(G) = \gamma(G) + 1$ are characterized.

Keywords: Domination number, complementary tree domination number, unicyclic graphs.

P.Vidhya
S.D.N.B.Vaishnav College for Women (Autonomous), Chennai, India.
E-mail: vidhya_lec@yahoo.co.in


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Article Type : Research Article
Title : Changing and Unchanging of Complementary Tree Domination Number in Graphs
Country : India
Authors : S.Muthammai || P.Vidhya

Abstract: A set $D$ of a graph $G = (V, E)$ is a dominating set if every vertex in $V-D$ is adjacent to some vertex in $D$. The domination number $\gamma(G)$ of $G$ is the minimum cardinality of a dominating set. A dominating set $D$ is called a complementary tree dominating set if the induced subgraph $$ is a tree. The minimum cardinality of a complementary tree dominating set is called the complementary tree domination number of $G$ and is denoted by $\gamma_{ctd}(G)$. The concept of complementary tree domination number in graphs is studied in \cite{a}. In this paper, we have studied the changing and unchanging of complementary tree domination number in graphs.

Keywords: Domination number, complementary tree dominating set, complementary tree domination number.

P.Vidhya
S.D.N.B.Vaishnav College for Women (Autonomous), Chennai, India.
E-mail: vidhya_lec@yahoo.co.in


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Article Type : Research Article
Title : Mathematical Expressions of Heat Transfer to MHD Oscillatory Flow and Homotopy Analysis Method
Country : India
Authors : V.Ananthaswamy || J.Soumyadevi || C.Thangapandi

Abstract: In this research paper we determine the combined effect of a transverse magnetic field and radiative heat transfer to unsteady flow of a conducting optically thin fluid through a channel filled with saturated porous medium and non-uniform walls temperature. The governing dimensionless equations are solved analytically and graphically. The approximate analytical expressions for the dimensionless axial velocity and temperature are obtained using the Homotopy analysis method. Also the analytical expressions for the shear stress function and the rate of heat transfer are also derived. The Homotopy analysis method has proven to be the best for solving complicated non-linear differential equations in MHD flow problems in engineering and applied sciences.

Keywords: Oscillatory flow; Porous medium; Heat transfer; Magnetic field; Homotopy analysis method.

V.Ananthaswamy
Department of Mathematics, The Madura College, Madurai, Tamil Nadu, India.
E-mail: ananthu9777@rediffmail.com


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Article Type : Research Article
Title : Stability of Quintic Functional Equation in 2-Banach Space
Country : India
Authors : R.Murali || M.Boobalan || A.Antony Raj

Abstract: In this paper, we investigate the Hyers-Ulam stability of the functional equation \begin{align}\label{e0} 2g(2x+y)+2g(2x-y)+g(x+2y)+g(x-2y)\nonumber\\ =20\left[g(x+y)+g(x-y)\right]+90g(x) \end{align} in 2-Banach space.

Keywords: Hyers-Ulam stability, 2-Banach space, Quintic functional equation.

R.Murali
Department of Mathematics, Sacred Heart College, Tirupattur, TamilNadu, India.
E-mail:


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Article Type : Research Article
Title : Intuitionistic Fuzzy $\ddot{g}$-Closed Sets
Country : India
Authors : N.Seenivasagan || O.Ravi || A.D.Ramesh Babu || M.Rajakalaivanan

Abstract: In this paper, we introduce the concepts of intuitionistic fuzzy $\ddot{g}$-closed sets and intuitionistic fuzzy $\ddot{g}$-open sets. Further, we study some of their properties.

Keywords: Intuitionistic fuzzy topology, Intuitionistic fuzzy $\ddot{g}$-closed set, Intuitionistic fuzzy $\ddot{g}$-open set.

O.Ravi
Department of Mathematics, P. M. Thevar College, Usilampatti, Madurai, Tamil Nadu, India.
E-mail: siingam@yahoo.com


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Article Type : Research Article
Title : Further study of $\omega$-closed sets
Country : India
Authors : O.Ravi || M.Rajakalaivanan || I.Rajasekaran

Abstract: In 1982, the notions of $\omega$-closed sets and $\omega$-open sets were introduced and studied by Hdeib \cite{ho82}. In 2009, Noiri et al \cite{namnw09} introduced some generalizations of $\omega$-open sets and investigated some properties of the sets. Moreover, they used them to obtain decompositions of continuity. Quite Recently Ravi et al \cite{rsrpa} studied further generalizations of $\omega$-open sets in topological spaces. In this paper we introduce new classes of functions in topological spaces and study the characterizations of such functions in detail. Finally we obtain some decomposition theorems.

Keywords: $\omega$-open set, $\alpha$-$\omega$-open set, pre-$\omega$-open set, $\beta$-$\omega$-open set, $\omega$-t-set, $\delta$-$\omega$-open set, semi$^\star$-$\omega$-closed set.

O.Ravi
Department of Mathematics, P. M. Thevar College, Usilampatti, Madurai, Tamil Nadu, India.
E-mail: siingam@yahoo.com


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