## April − June (2015)Article in Press

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 Article Type : Research Article Title : Further Decompositions of $rg$-Continuity Country : India Authors : K. M. Dharmalingam || P. Ramesh || O. Ravi

Abstract: In [12], Sundaram and Rajamani obtained three decompositions of $rg$-continuity. In this paper, we obtain three further decompositions of $rg$-continuity.

Keywords: $r\alpha g$-continuity, $gpr$-continuity, $C_r$-continuity, $C_r^*$-continuity and $rg$-continuity.

O. Ravi
E-mail: siingam@yahoo.com.

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 Article Type : Research Article Title : $g^\star$-Closed Sets with Respect to an Ideal Country : India Authors : K. M. Dharmalingam || D. Bharathi || O. Ravi

Abstract: In [12], An ideal on a set X is a non empty collection of subsets of X with heredity property which is also closed under finite unions. The concept of generalized closed ($g$-closed) sets was introduced by Levine \cite{lg70}. Quite Recently, Jafari and Rajesh \cite{jr11} have introduced and studied the notion of generalized closed ($g$-closed) sets with respect to an ideal. Many generalizations of $g$-closed sets are being introduced and investigated by modern researchers. One among them is $g^\star$-closed sets which were introduced by Veerakumar \cite{vee}. In this paper, we introduce and investigate the concept of $g^\star$-closed sets with respect to an ideal.

Keywords: Topological space, open set, $g^\star$closed set, $g$-closed set, $\mathcal{I}_{g}$-closed set, $\mathcal{I}_{\pi g}$-closed set, ideal.

O. Ravi
E-mail: siingam@yahoo.com.

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 Article Type : Research Article Title : $\tilde{g}$(1,2)*-closed Sets in Bitopological Spaces Country : India Authors : K. M. Dharmalingam || A. Thamilisai || O. Ravi

Abstract: In this paper, we offer a new class of sets called $\tilde{g}$(1,2)*-closed sets in bitopological spaces and we study some of its basic properties. It turns out that this class lies between the class of $\tau$$_{1,2}$-closed sets and the class of (1,2)*-g-closed sets.

Keywords: Bitopological space, (1,2)*-$\hat{g}$-closed set, (1,2)*-$\ddot{g}$-closed set, (1,2)*-g-closed set, (1,2)*-$\ddot{g}_\alpha$-closed set.

O. Ravi
E-mail: siingam@yahoo.com.

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 Article Type : Research Article Title : Another generalized Closed Sets in Ideal Topological Spaces Country : India Authors : O. Ravi || R. Asokan || A. Thiripuram

Abstract: Characterizations and properties of $\mathcal{I}_{g\delta}$-closed sets and $\mathcal{I}_{g\delta}$-open sets are given. A characterization of $\delta$-$\star$-normal spaces is given in terms of $\mathcal{I}_{g\delta}$-open sets.

Keywords: $g\delta$-closed set, $\mathcal{I}_{g\delta}$-closed set, $\star$-closed set, $\mathcal{I}_{\pi g}$-closed set, $\mathcal{I}_g$-closed set.

O. Ravi
E-mail: siingam@yahoo.com.

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 Article Type : Research Article Title : Weakly (1,2)*-$g^*$-closed Sets Country : India Authors : K. M. Dharmalingam || G. Thanavalli || O. Ravi

Abstract: The aim of this paper is to introduce a new class of (1,2)*-generalized closed sets called weakly (1,2)*-$g^*$-closed sets which contains the above mentioned class.

Keywords: (1,2)*-$g^*$-closed set, (1,2)*-w$g^*$-closed set, (1,2)*-$g^*$-continuous map, (1,2)*-$g^*$-irresolute map, weakly (1,2)*-$g^*$-open map, weakly (1,2)*-$g^*$-continuous map.

O. Ravi
E-mail: siingam@yahoo.com.

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 Article Type : Research Article Title : The number of homomorphisms from quaternion group into some finite groups Country : India Authors : R. Rajkumar || M. Gayathri || T. Anitha

Abstract: We derive general formulae for counting the number of homomorphisms from quaternion group into each of quaternion group, dihedral group, quasi-dihedral group and modular group by using only elementary group theory.

Keywords: Finite groups, Homomorphisms.

R. Rajkumar
Department of Mathematics, The Gandhigram Rural Institute--Deemed University, Gandhigram, Tamil Nadu, India.
E-mail: rrajmaths@yahoo.co.in.

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 Article Type : Research Article Title : Characterization of the Generalized Weibull-Gompertz Distribution Based on the Upper Record Values Country : Egypt Authors : A. H. El-Bassiouny || M.EL-Damcese || A.Mustafa || M. S. Eliwa

Abstract: This paper introduces characterization of the generalized Weibull-Gompertz distribution based on the upper record values. Several properties are studied in this paper such as reversed (hazard) function, moments, maximum likelihood estimation, mean residual (past) lifetime. A real data set is analyzed.

Keywords: Upper record values, reversed (hazard) function, generalized Weibull-Gompertz distribution, mean residual (past) lifetime.

M. S. Eliwa
Mathematics Department, Faculty of Science, Mansoura University, Egypt.
E-mail: msabereliwa@mans.edu.eg.

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 Article Type : Research Article Title : Switching of a Vertex in Path and $b$-coloring Country : India Authors : Samir K. Vaidya || Minal S. Shukla

Abstract: A proper coloring in which every color class has a vertex adjacent to at least one vertex in every other color classes is called $b$-coloring. The $b$-chromatic number of a graph is the largest integer for which graph admits a $b$-coloring. We investigate the $b$-chromatic number for the graphs obtained from path by means of switching of a vertex.

Keywords: Coloring, b-coloring, b-continuity.

Samir K. Vaidya
Department of Mathematics, Saurashtra University, Rajkot, Gujarat, India.
E-mail: samirkvaidya@yahoo.co.in.

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 Article Type : Research Article Title : The Minimum Maximal Domination Energy of a Graph Country : India Authors : A. C. Dinesh || Puttaswamy

Abstract:

Keywords: minimum maximal dominating set, minimum maximal domination matrix, minimum maximal eigenvalues, minimum maximal energy of a graph.

Puttaswamy
2Department of Mathematics, P.E.S.College of Engineering, Mandya, India.
E-mail: puttaswamy@gmail.com.

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 Article Type : Research Article Title : Exponentiated Flexible Weibull Extension Distribution Country : Egypt Authors : A. El-Gohary || A. H. El-Bassiouny || M. El-Morshedy

Abstract: In this paper, a new three parameter model is introduced. We called it the exponentiated flexible Weibull extension (EFW) distribution. Several properties of this distribution have been discussed. The maximum likelihood estimators of the parameters are derived. Two real data sets are analyzed using the new model, which show that the new model fits the data better than some other very well known models.

Keywords: Weibull Distribution\textbf{, }Hazard function, Maximum likelihood estimators, Median and mode.

M. El-Morshedy
Department of Mathematics, College of Science, Mansoura University, Mansoura, Egypt.
E-mail: mah_elmorshedy@yahoo.com.

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 Article Type : Research Article Title : Some Results on Odd Mean Graphs Country : India Authors : S. Suganthi || R. Vasuki || G. Pooranam

Abstract: Let $G=(V,E)$ be a graph with $p$ vertices and $q$ edges. A graph $G$ is said to have an odd mean labeling if there exists a function $f:V(G)\rightarrow\{0,1,2,\dots,2q-1\}$ satisfying $f$ is $1$-$1$ and the induced map $f^*:E(G)\rightarrow\{1,3,5,\dots,2q-1\}$ defined by $f^*(uv)=\left\{\begin{array}{ll}\frac{f(u)+f(v)}{2}&\quad\mbox{if f(u)+f(v) is even}\\ \frac{f(u)+f(v)+1}{2}&\quad\mbox{if f(u)+f(v) is odd.}\end{array}\right.$ is a bijection. A graph that admits an odd mean labeling is called an odd mean graph. In this paper, we prove that the graphs slanting ladder $SL_n$ for $n\geq 2,$ $Q_n\odot K_1$ for $n\geq 1,$ $TW(P_{2n})$ for $n\geq 2, H_n\odot mK_1$ for all $n\geq 1, m\geq 1$ and $mQ_3$ for $m\geq 1$ are odd mean graphs.

Keywords: Labeling, odd mean labeling, odd mean graph.

R. Vasuki
Department of Mathematics, Dr. Sivanthi Aditanar College of Engineering, Tiruchendur, Tamil Nadu, India.
E-mail: vasukisehar@gmail.com.

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 Article Type : Research Article Title : Counting Homomorphisms From Quasi-dihedral Group into Some Finite Groups Country : India Authors : R. Rajkumar || M. Gayathri || T. Anitha

Abstract: We derive general formulae for counting the number of homomorphisms from quasi-dihedral group into each of quasi-dihedral group, quaternion group, dihedral group, and modular group by using only elementary group theory.

Keywords: Finite groups, Homomorphisms.

R. Rajkumar
Department of Mathematics, The Gandhigram Rural Institute--Deemed University, Gandhigram, Tamil Nadu, India.
E-mail: rrajmaths@yahoo.co.in.

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 Article Type : Research Article Title : Enumeration of Homomorphisms From Modular Group into Some Finite Groups Country : India Authors : R. Rajkumar || M. Gayathri || T. Anitha

Abstract: We derive general formulae for counting the number of homomorphisms from modular group into each of modular group, dihedral group, quaternion group and quasi-dihedral group by using only elementary group theory.

Keywords: Finite groups, Homomorphisms.

R. Rajkumar
Department of Mathematics, The Gandhigram Rural Institute--Deemed University, Gandhigram, Tamil Nadu, India.
E-mail: rrajmaths@yahoo.co.in.

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Abstract: In this paper, we introduce (1,2)*-Fuzzy generalized continuous maps and (1,2)*-Fuzzy$\ddot{{g}}$ continuous maps and study their relations with existing generalized (1,2)*-Fuzzy continuous maps.
Keywords: Fuzzy bitopological space,(1,2)*-fuzzy g- continuous maps, (1,2)*-fuzzy$\ddot{{g}}$-continuous maps.