Haslinda Ibrahim

A note on \The nearest symmetric fuzzy solution for a symmetric fuzzy linear system"

Abstract This paper provides accurate approximate solutions for the symmetric fuzzy linear systems in (Allahviranloo et al:[1]).

Combinatorial design for a conference: constructing a balanced three-parallel session schedule

Abstract In this paper, we present some well known results in combinatorial design theory. Next, we will use these results to construct a balanced three-parallel session schedule for a conference. A conference normally contains a set of sessions (each one of them involving three fields) that has to be scheduled within a time period of k days. The problem consists of finding a balanced schedule for each field.

On the cyclic decomposition of complete multigraph into near Hamiltonian cycles

Let v and λ be positive integer, λKv denote a complete multigraph. A decomposition of a graph G is a set of subgraphs of G whose edge sets partition the edge set of G. In this article, difference set method is used to introduce a new design that is decomposed a complete multigraph into near Hamiltonian cycles. In course of developing this design, a combination between near-4-factor and a cyclic (v − 1)-cycle system of 4Kv, when v = 4n + 2, n > 2, will be constructed.

On cyclic near-Hamiltonian cycle system of the complete multigraph

A cycle system of λKv is Hamiltonian when each of its cycles passes through all vertices of λKv. In this paper, we propose a new type of cycle system called near-Hamiltonian cycle system of λKv which has all its cycles of length (v − 1). We are concerned with a cyclic near-Hamiltonian cycle system of 2K4n+1. Then we provide a construction method for such cyclic cycle system by using difference method.

Determining distinct circuit in complete graphs using permutation

A Half Butterfly Method (HBM) is a method introduced to construct the distinct circuits in complete graphs where used the concept of isomorphism. The Half Butterfly Method was applied in the field of combinatorics such as in listing permutations of n elements. However the method of determining distinct circuit using HBM for n > 4 is become tedious. Thus, in this paper, we present the method of generating distinct circuit using permutation.A Half Butterfly Method (HBM) is a method introduced to construct the distinct circuits in complete graphs where used the concept of isomorphism. The Half Butterfly Method was applied in the field of combinatorics such as in listing permutations of n elements. However the method of determining distinct circuit using HBM for n > 4 is become tedious. Thus, in this paper, we present the method of generating distinct circuit using permutation.

Enumeration Class of Polyominoes Defined by Two Column

Abacus diagram is a graphical representation for any partition μ of a positive integer t. This study presents the bead positions as a unite square in the graph and de ne a special type of e-abacus called nested chain abacus N which is represented by the connected partition. Furthermore, we redefined the polyominoes as a special type of e-abacus diagram. Also, this study reveals new method of enumerating polyominoes special design when e=2. Mathematics Subject Classification: 05A15

Some modifications of Sarrus’s rule method via permutation for finding determinant of 4 by 4 square matrix

Sarrus rule is well known method for finding determinant of square matrix. This method is also known as a cross multiplication method. However this method is not applicable for n > 3. With this motivation, we attempt to extend this method by employing some modifications using permutation for the case of 4 by 4 square matrix

Application of half butterfly method in listing permutation

A Half Butterfly Method is a new method introduced to construct the distinct circuits in complete graphs where used the concept of isomorphism. The Half Butterfly Method can be applied in the field of combinatorics such as in listing permutations of n elements. Thus, in this paper, we presented a permutation generation using Half Butterfly Method.

Embedding the outer chain movement for main partition of β-number with length [1, 0, 0,…]

One of the graphical representations for any partition of a non-negative integers in the modular representation theory of diagram algebra is James abacus using Beta numbers. In this work James abacus is divided positions into several chains. A new diagram Atco is introduced by employing on the outer chain with length [1, 0, 0,…] on the active James abacus. Finally a consecutive new diagram of b2, b3,…, be can be found from active diagram Atco which is found after applying chain movement.

Embedding chain movement in James Diagram for partitioning beta number

James Diagram is a graphical representation for partition any non-negative numbers. In this paper new diagrams Atc are constructed by embedding a chain movement. The first Beta numbers are obtained from the partition and denoted by b1. Then b2 is obtained from b1. Finally, this method is generalized to any bn from b1 where e = 2 and x ∈  [(fix(βi2)+1),1].