Contemporary Mathematics and Applications (ConMathA)

Molecular Topology Index of a Zero Divisor Graph on a Ring of Integers Modulo Prime Power Order

2024-05-13T09:35:42+07:00

In chemistry, graph theory has been widely utilized to address molecular problems, with numerous applications in graph theory and ring theory within this field. One of these applications involves topological indices that represent chemical structures with numerical values. Various types of topological indices exist, including the Wiener index, the first Zagreb index, and the hyper-Wiener index. In the context of this research, the values of the Wiener index, the first Zagreb index, and the hyper-Wiener index for zero-divisor graphs on the ring of integers modulo a prime power order will be explored through a literature review and conjecture.

Biplot Analysis of Life Satisfaction Dimensions in the Happiness Index

2024-01-11T14:08:11+07:00

The main goal of every individual in life is to achieve happiness, a subjective concept. To measure happiness, one approach used is the life satisfaction dimension. In multivariate analysis, the biplot method emerges as a useful tool to map variables and objects of observation simultaneously in a two-dimensional graph. This study was conducted with the aim of analyzing biplots on the happiness index, with the dimension of life satisfaction as the main variable. The data used comes from the Central Bureau of Statistics (BPS), specifically related to the Life Satisfaction Dimension of the Happiness Index in 2021. By conducting careful biplot analysis, the pattern of relationships between provinces in the context of happiness can be revealed. The results of the biplot analysis show that provinces in the same quadrant have closer similarities in happiness characteristics than provinces in different quadrants.

Rainbow Connection on Amal(Fn,xz,m) Graphs and Amal(On,xz,m) Graphs

2024-05-15T09:38:50+07:00

Coloring graph is giving a color to a set of vertices and a set of edges on a graph. The condition for coloring a graph is that each color is different for each neighboring member graph. Coloring graph can be done by mapping a different color to each vertex or edge. Rainbow coloring is a type of rainbow connected with coloring edge. It ensures that every graph G has a rainbow path. A rainbow path is a path in a graph where no two vertices have the same color. The minimum number of colors in a rainbow connected graph is called the rainbow connection number denoted by rc(G). The graphs used in this study are the Amal(F_n,xz,m) graph and the Amal(O_n,xz,m) graph.

Implementation of K-Means and Single Linkage on Types of Disabilities in East Java Province

2024-07-15T08:58:47+07:00

The high number of people with disabilities is one of the problems faced by the Indonesian government, especially in Java Province. After West Java Province, East Java Province is in second place as the province with the highest rate of people with disabilities in Indonesia. Disabled people are people with physical disabilities such as not being able to walk, not being able to talk, not being able to see, and so on. The aim of this research is to group districts in East Java Province based on types of disabilities with the hope of facilitating activities in fulfilling the rights of people with disabilities in East Java Province. The grouping was carried out in order to determine the characteristics of each cluster using so that the optimal k-means method was used for clustering using the Euclidean distance method with cluster 1 in 29 districts and cluster 2 in 9 districts. The most optimal single linkage uses the Euclidean distance method with cluster 1 having 8 districts and cluster 2 having 30 districts. From the results of the validity index values, it was found that the single linkage method had the smallest validity value of the icdrate method compared to the k-means method.

Existence and Uniqueness of Homogeneous Linear Equation Solutions in Supertropical Algebra

2024-09-29T20:09:53+07:00

This research investigates the existence and uniqueness of solutions to homogeneous linear equations in supertropical algebra. We analyze the structure of supertropical matrices to identify the conditions in which nontrivial solutions exist for the system of equations A⊗𝒙 ⊨ 𝜀, where A is a matrix over a supertropical semiring and x is a vector. By applying determinant-based criteria, we demonstrate how tropical and supertropical values influence the solution space. The research applies theorems that determine the presence of trivial and nontrivial solutions and uses examples to illustrate practical methods for solving homogeneous matrix systems. This highlights the distinct characteristics of supertropical algebra compared to classical linear algebra. Our findings provide a deeper insight into solution behaviors in supertropical systems, paving the way for further research in tropical mathematics.