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Description Details Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are:
Smarandache multi-spaces with applications to other sciences, such as those of algebraic multi-systems, multi-metric spaces,. . . , etc.. Smarandache geometries;
Differential Geometry; Geometry on manifolds;
Topological graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph and map enumeration; Combinatorial designs; Combinatorial enumeration;
Low Dimensional Topology; Differential Topology; Topology of Manifolds;
Geometrical aspects of Mathematical Physics and Relations with Manifold Topology;
Applications of Smarandache multi-spaces to theoretical physics; Applications of Combinatorics to mathematics and theoretical physics;
Mathematical theory on gravitatio...

Excerpt Details Duality Theorems of Multiobjective
Generalized Disjunctive Fuzzy Nonlinear Fractional Programming
Abstract: This paper is concerned with the study of duality conditions to convex-concave generalized multiobjective fuzzy nonlinear fractional disjunctive programming problems for which the decision set is the union of a family of convex sets. The Lagrangian function for such problems is defined and the Kuhn-Tucker Saddle and Stationary points are characterized. In addition, some important theorems related to the Kuhn-Tucker problem for saddle and stationary points are established. Moreover, a general dual problem is formulated together with weak; strong and converse duality theorems are proved.
Key Words: Generalized multiobjective fractional programming; Disjunctive programming; Convexity; Concavity; fuzzy parameters Duality.
...

Table of Contents Details Contents
Duality Theorems of Multiobjective Generalized Disjunctive Fuzzy Nonlinear
Fractional Programming BY E.E.AMMAR . . . . . . . . . . . . . . . . . . . . 01
Surface Embeddability of Graphs via Joint Trees
BY YANPEI LIU. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15
Plick Graphs with Crossing Number 1
BY B.BASAVANAGOUD AND V.R.KULLI . . . . . . . . . . . . . . . . . . . . . . 21
Effects of Foldings on Free Product of Fundamental Groups
BY M.El-GHOUL, A. E.El-AHMADY, H.RAFAT AND M.ABU-SALEEM. . . . . . . 29
Absolutely Harmonious Labeling of Graphs
BY M.SEENIVASAN AND A.LOURDUSAMY . . . . . . . . . . . . . . . . . . . . 40
The Toroidal Crossing Number of K4n
BY SHENGXIANG LV, TANG LING AND YUANGQIU HUANG . . . . . . . . . . 52
On Pathos Semitotal and Total Block Graph of a Tree
BY MUDDEBIHAL M. H. AND SYED BABAJAN. . . . . . . . . . . . . . . . . . 64
Varieties of Groupoids and Quasigroups Generated by Linear-Bivariate
Polynomials Over Ring Zn BY E.ILOJIDE, T.G.JAIYEOLA AND O.O.OWOJORI . . . . . 79
New Characterizations for Bertrand Curves in Minkowski 3-Space
BY BAHADDIN BUKCU, MURAT K...

Description Details In The 2nd Conference on Combinatorics and Graph Theory of China (Aug. 16-19, 2006, Tianjing), I formally presented a combinatorial conjecture on mathematical sciences (abbreviated to CC Conjecture), i.e., a mathematical science can be reconstructed from or made by combinatorialization, implicated in the foreword of Chapter 5 of my book Automorphism groups of Maps, Surfaces and Smarandache Geometries (USA, 2005). This conjecture is essentially a philosophic notion for developing mathematical sciences of 21st century, which means that we can combine different fields into a union one and then determines its behavior quantitatively. It is this notion that urges me to research mathematics and physics by combinatorics, i.e., mathematical combinatorics beginning in 2004 when I was a post-doctor of Chinese Academy of Mathematics and System Science. It finally brought about me one self-contained book, the first edition of this book, published by InfoQuest Publisher in 2009. This edition is a revisited edition, also includes the development of a few topics discussed in the first edition....

Excerpt Details 1.5 ENUMERATION TECHNIQUES
1.5.1 Enumeration Principle. The enumeration problem on a finite set is to count and find closed formula for elements in this set. A fundamental principle for solving this problem in general is on account of the enumeration principle: For finite sets X and Y , the equality |X| = |Y | holds if and only if there is a bijection f : X → Y . Certainly, if the set Y can be easily countable, then we can find a closed formula for elements in X....

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