## Issue 3 − DVolume 3 (2015)

ISSUE 3 − A ISSUE 3 − B ISSUE 3 − C ISSUE 3 − D
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 Article Type : Research Article Title : Strongly Prime Labeling For Some Graphs Country : India Authors : S.Meena || P.Kavitha

Abstract: A graph $G=(V,E)$ with $\, n$ vertices is said to admit prime labeling if its vertices can be labeled with distinct positive integers not exceeding, n such that the label of each pair of adjacent vertices are relatively prime. A graph $G$ which admits prime labeling is called a prime graph and a graph $G$ is said to be a strongly prime graph if for any vertex, $v$ of $G$ there exists a prime labeling, f satisfying, $f\left(v\right)=1$. In this paper we prove that the graphs corona of triangular snake, corona of quadrilateral snake, corona of ladder graph and a graph obtained by attaching $P_{2}$ at each vertex of outer cycle of prism $D_{n}$ by $(D_{n} ;P_{2})$, helm, gearwheel are strongly prime graphs.

Keywords: Prime Labeling, Prime Graph, Strongly Prime Graph.

P.Kavitha
Department of Mathematics, S.R.M University, Chennai, Tamil Nadu, India.
E-mail: kavithavps@gmail.com

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 Article Type : Research Article Title : Folding of Digraphs Country : Egypt Authors : E. M. Elkholy || A. Sakr || H. Ahmed

Abstract: In this paper we introduced the definition of dibipartite graphs, complete dibipartite graphs and digraph folding, then we proved that any dibipartite graph can be folded but the complete dibiparatite graph can be folded to an arc. By using adjacency matrices we described the digraph folding.

Keywords: Digraphs, dibipartite graphs, complete dibipartite graphs, folding of dibipartite graphs and adjacency matrices.

E. M. Elkholy
Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt.
E-mail: pro.entsarelkholy809@yahoo.com

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 Article Type : Research Article Title : Multiplication Formulae for Double Hypergeometric Functions of Exton and Kampe Deferiet Country : India Authors : M.I.Qureshi || K.A.Quraishi || B.Khan || R.Singh

Abstract: In this paper, we obtain two multiplication formulae for double hypergeometric functions of Exton and Kamp\'{e} de F\'{e}riet, by the application of Rainville's theorem on generating function.

Keywords: Pochhammer's symbol; Multiplication formulae, Double and triple hypergeometric functions; Generating function; Series iteration technique.

K.A.Quraishi
Mathematics Section, Mewat Engineering College (Waqf), Palla, Nuh, Mewat, Haryana, India.
E-mail: kaleemspn@yahoo.co.in

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 Article Type : Research Article Title : Graceful Labeling for Swastik Graph Country : India Authors : V J Kaneria || H M Makadia

Abstract: We investigate a new graph which is called swastik graph. We proved that the swastik graph is graceful. We have investigated some swastik graph related families of connected graceful graphs. We proved that path union of swastik graph, cycle of swastik graph and star of swastik graph are graceful.

Keywords: Graceful labeling, swastik graph, path union of graphs, cycle of graphs, star of a graph.

Govt. Engineering College, Rajkot-360005, India.

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 Article Type : Research Article Title : $\tilde{g}$-Closed Sets in Ideal Topological Spaces Country : India Authors : R. Asokan || O. Ravi || I. Rajasekaran || R. Sathiyapriya

Abstract: The notion of $\tilde{g}$-closed sets is introduced in ideal topological spaces. Characterizations and properties of $\mathcal{I}_{\tilde{g}}$-closed sets and $\mathcal{I}_{\tilde{g}}$-open sets are given. A characterization of normal spaces is given in terms of $\mathcal{I}_{\tilde{g}}$-open sets. Also, it is established that an $\mathcal{I}_{\tilde{g}}$-closed subset of an $\mathcal{I}$-compact space is $\mathcal{I}$-compact.

Keywords: $\tilde{g}$-closed set, $\mathcal{I}_{\tilde{g}}$-closed set and $\mathcal{I}$-compact space.

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

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 Article Type : Research Article Title : A Study on M/G/1 Queueing System with Extended Vacation, Random Breakdowns and General Repair Country : India Authors : S.Maragathasundari || K.Karthikeyan

Abstract: This Paper study about a Non Markovian queueing model with general vacation, Random breakdown followed by a repair process .An additional aspect of Extended vacation is considered here. After a service completion, the server takes a vacation. The server has the option to take an extended vacation after general vacation or the server may continue to stay in the system to serve the customers. It is assumed that customers arrive at the system one by one. Vacation time, extended vacation time and repair time follows general distribution.Steady state results in explicit and closed form in terms of the probability generating functions for the number of customers in the queue, average number of customers, and the average waiting time in the queue are derived.

Keywords: Random breakdown, Repair process, Extended vacation, Steady state, Queue size distribution.

S.Maragathasundari
Department of Mathematics, Velammal Institute of Technology, Chennai, India.
E-mail: maragatham01@gmail.com

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 Article Type : Research Article Title : On Goldberg $q^{th}$ Order and Goldberg $q^{th}$ Type of an Entire Function Represented by Multiple Dirichlet Series Country : India Authors : Udai Veer Singh || Anupma Rastogi

Abstract: In this paper we consider entire function represented by multiple Dirichlet series in several complex variables. Also consider product of the class of entire function, we then characterized the $q^{th}$ order and $q^{th}$ type of an entire function represented and express in terms of its coefficient and exponent.

Keywords: Entire function, Multiple Dirichlet series, Golídberg order, Golídberg type.

Anupma Rastogi
Department of Mathematics and Astronomy, University of Lucknow, Lucknow, India.
E-mail: anupmarastogi13121993@gmail.com

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 Article Type : Research Article Title : Applications of Semi $^{\#}$g$\alpha$-closed Sets in Topological Spaces Country : India Authors : V.Kokilavani || M.Vivek Prabu

Abstract: In this paper, we define some new sets namely semi $^\#$g$\alpha$-border, semi $^{\#}$g$\alpha$-frontier and semi $^{\#}$g$\alpha$-exterior which are denoted by semi $^{\#}$g$\alpha$-bd(A), semi $^{\#}$g$\alpha$-fr(A) and semi $^{\#}$g$\alpha$-ext(A), where A is any subset of X. We also examine the basic properties of these sets.

Keywords: Semi $^{\#}$g$\alpha$-closed set, Semi $^{\#}$g$\alpha$-open set, Semi $^{\#}$g$\alpha$-closure, Semi $^{\#}$g$\alpha$-interior, Semi $^{\#}$g$\alpha$-border, Semi $^{\#}$g$\alpha$-frontier and Semi $^{\#}$g$\alpha$-exterior.

M.Vivek Prabu
Department of Mathematics, Kongunadu Arts and Science College (Autonomous), Coimbatore, Tamilnadu, India.
E-mail: kavithai.vivek@yahoo.in

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 Article Type : Research Article Title : $\pi g\alpha\;$ Closed Mappings in Intuitionistic Fuzzy Topological Spaces Country : India Authors : N. Seenivasagan || O. Ravi || S. Satheesh Kanna

Abstract: In this paper, we introduce the concepts of intuitionistic fuzzy $\pi$g$\alpha$ closed mappings and intuitionistic fuzzy i-$\pi$g$\alpha$ closed mappings. Further, we study some of their properties.

Keywords: Intuitionistic fuzzy topology, Intuitionistic fuzzy $\pi$g$\alpha$ closed set, Intuitionistic fuzzy $\pi$g$\alpha$ closed mapping and Intuitionistic fuzzy i-$\pi$g$\alpha$ closed mapping.

S. Satheesh Kanna
Department of Mathematics, Bharathidasan University, Thiruchirapalli, Tamil Nadu, India.
E-mail: satheesh$_-$kanna@yahoo.co.in

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Abstract: A graph \textit{G }$=(V,E)$ with p vertices and q edges is said to have skolem difference mean labeling if it is possible to label the vertices x$\varepsilon V$ with distinct elements \textit{f}$(x)$from the set$\lbrace 1,2,3,\ldots ,p+q\rbrace$ in such a way that the edge \textit{e}$=uv$\textit{ }is labeled with $\frac{\vert f(u)-f(v)\vert }{2}$ if $\vert f(u)-f(v)\vert$ is even and $\frac{\vert f(u)-f(v)\vert +1}{2}$ if $\vert f(u)-f(v)\vert$ is odd and the resulting labels of the edges are distinct and are from $\lbrace 1,2,3,\ldots ,q\rbrace$. A graph that admits skolem difference mean labeling is called a skolem difference mean graph. In this paper, the author studied some results on skolem difference mean graphs.