GENERAL MATHEMATICS NOTES

Vol. 5, No. 2, August 2011 

Contents

Title: Cantor Theorem and Application in Some Fixed Point Theorems in a Generalized Metric Space

Authors: Babli Saha and A. P. Baisnab

Abstract: Some useful fixed point Theorems are derived by applying Cantor like Theorem as proved in complete generalized metric spaces.

PP. 1-7

Title: E-Cordial and Z₃-Magic Labelings in Extended Triplicate Graph of a Path

Authors: E. Bala and K. Thirusangu

Abstract: In this paper we prove that the extended triplicate graph (ETG) of finite paths admits product E-cordial, total product E-cordial labelings. We show that ETG of finite paths of length n where  n ∉ {4m-3|m∈N} admits  E-Cordial, total E-cordial labelings and also  we prove the existence of Z₃ – magic labeling for the modified  Extended Triplicate graph.

PP. 8-23

Title: Covering Cover Pebbling Number for Even Cycle Lollipop

Authors: A. Lourdusamy, S. Samuel Jeyaseelan and T. Mathivanan

Abstract: In a graph G with a distribution of pebbles on its vertices, a pebbling move is the removal of two pebbles from one vertex and the addition of one pebble to an adjacent vertex. The covering cover pebbling number, denoted by σ(G), of a graph G, is the smallest number of pebbles, such that, however the pebbles are initially placed on the vertices of the graph, after a sequence pebbling moves, the set of vertices with pebbles forms a covering of G. In this paper we determine the covering cover pebbling number for cycles and even cycle lollipops.

PP. 24-41

Title: On Pebbling Jahangir Graph

Authors: A. Lourdusamy, S. Samuel Jeyaseelan and T. Mathivanan

Abstract: Given a configuration of pebbles on the vertices of a connected graph G, a pebbling move (or pebbling step) is defined as the removal of two pebbles off a vertex and placing one on an adjacent vertex. The pebbling number, f(G), of a graph G is the least number m such that, however m pebbles are placed on the vertices of G, we can move a pebble to any vertex by a sequence of pebbling moves. In this paper, we determine f(G) for Jahangir graph J2,m (m ≥ 8).

PP. 42-49

Title: On Smarandache TN Curves in Terms of Biharmonic Curves in the Special Three-Dimensional φ-Ricci Symmetric Para-Sasakian Manifold ℙ

Authors: Talat Körpinar and Essin Turhan

Abstract: In this paper, we study SmarandacheTN curves in terms of spacelike biharmonic curves in the special three-dimensional φ-Ricci symmetric para-Sasakian manifold ℙ. We define a special case of such curves and call it Smarandache TN curves in the special three-dimensional φ-Ricci symmetric para-Sasakian manifold ℙ. We construct parametric equations of Smarandache TN curves in terms of biharmonic curve in the special three-dimensional $\phi$-Ricci symmetric para-Sasakian manifold ℙ.

PP. 50-58

Title: Biharmonic Curves IN ℍ²×ℝ

Authors: Talat Körpinar and Essin Turhan

Abstract: In this paper, we study biharmonic curves in the ℍ²×ℝ. We show that all of them are helices. By using the curvature and torsion of the curves, we give some characterizations biharmonic curves in the ℍ²×ℝ.

PP. 59-66

Title: Bertrand Mate of Biharmonic Reeb Curves in 3-Dimensional Kenmotsu Manifold

Authors: Talat Körpinar, Gülden Altay and Essin Turhan

Abstract: In this article, we study biharmonic Reeb curves in 3-dimensional Kenmotsu manifold. Moreover, we apply biharmonic Reeb curves in special 3-dimensional Kenmotsu manifold K. Finally, we characterize Bertrand mate of the biharmonic Reeb curves in terms of their curvature and torsion in special 3-dimensional Kenmotsu manifold K.

PP. 67-74