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Issue 3 − D
Volume 3 (2015)

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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.

H M Makadia

Govt. Engineering College, Rajkot-360005, India.

E-mail: makadia.hardik@yahoo.com

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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, GolĂdberg order, GolĂdberg 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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Article Type |
: | Research Article |

Title |
: | Some Results on Skolem Difference Mean Graph |

Country |
: | India |

Authors |
: | K.Murugan |

**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.

**Keywords: ** Skolem difference mean labeling, skolem difference mean graph.

K.Murugan

Postgraduate and Research Department of Mathematics, The M.D.T. Hindu College, Tirunelveli, Tamilnadu, India.

E-mail: muruganmdt@gmail.com