Jurnal Matematika MANTIK

Developing A Secure Cryptosystem with Rainbow Vertex Antimagic Coloring of Cycle Graph

Marsidi Marsidi — Thu, 01 Dec 2022 00:00:00 +0000

An edge labeling of graph G is a function g from the edge set of graph G to the first natural numbers up to the number of the edge set. Graph G admits a rainbow vertex antimagic coloring if, for any two vertices, there is a path with different colors of all internal vertices. The vertex color of graph G is assigned by vertex weight. The vertex weight of graph G is obtained by summing all edge labels that incident with that vertex. The rainbow vertex antimagic connection number of graph G, denoted by rvac(G) is the smallest number of different colors induced by rainbow vertex antimagic coloring. In this research, we determine the upper bound of the rainbow vertex antimagic connection number (rvac) on a cycle graph (Cn) and create a secured cryptosystem using a modified Affine Cipher based on rainbow vertex antimagic coloring.

Mixed Boundary Value Problem for Nonlinear Fractional Volterra Integral Equation

Faraj Y. Ishak — Sat, 31 Dec 2022 00:00:00 +0000

In this paper we present the existence of solutions for a nonlinear fractional integral equation of Volterra type with mixed boundary conditions, some necessary hypotheses have been developed to prove the existence of solutions to the proposed equation. Krasnoselskii Theorem, Banach Contraction principle, and Leray-Schauder degree theory are the basic theorems used here to find the results. A simple example of the application of the main result is presented.

On the Relation of the Total Graph of a Ring and a Product of Graphs

Mohammad Nafie Jauhari — Sat, 31 Dec 2022 00:00:00 +0000

The total graph of a ring R, denoted as T(Γ(R)), is defined to be a graph with vertex set V(T(Γ(R)))=R and two distinct vertices u,v∈V(T(Γ(R))) are adjacent if and only if u+v∈Z(R), where Z(R) is the zero divisor of R. The Cartesian product of two graphs G and H is a graph with the vertex set V(G×H)=V(G)×V(H) and two distinct vertices (u_1,v_1 ) and (u_2,v_2 ) are adjacent if and only if: 1) u_1=u_2 and v_1 v_2∈H; or 2) v_1=v_2 and u_1 u_2∈E(G). An isomorphism of graphs G dan H is a bijection ϕ:V(G)→V(H) such that u,v∈V(G) are adjacent if and only if f(u),f(v)∈V(H) are adjacent. This paper proved that T(Γ(Z_2p )) and P_2×K_p are isomorphic for every odd prime p.

Existence and Uniqueness of Fixed Points in Cone Metric Spaces for ω-distance

Ahmad Khairul Umam, Nihaya Alivia C. Dewi, Pukky Tetralian B. Ngastiti — Sat, 31 Dec 2022 00:00:00 +0000

Simulation Of The K-Means Clustering Algorithm With The Elbow Method in Making Clusters Of Provincial Poverty Levels in Indonesia

Joko Riyono, Christina Eni Pujiastuti — Sat, 31 Dec 2022 00:00:00 +0000

One way to ensure that government programs and assistance for each province are right on target is to create a model of grouping or clustering provinces in Indonesia based on poverty levels. Algorithm K Means is one of the clustering methods in Data Mining to divide n observations into k groups so that each observation is in the group with the closest mean. In this study, provincial poverty level clustering in Indonesia will be made based on three poverty level indicators, namely the Percentage of Poor Population (P0), Poverty Depth (P1), and Poverty Severity (P2) with the K-Means Algorithm using the Elbow Method assisted by the Python Program. The results obtained are 5 optimal clusters of provincial poverty rates in Indonesia.

A New analytical Modeling for Fractional Telegraph Equation Arising in Electromagnetic

Muhammad Amin Sadiq Murad, Mudhafar Hamed Mamadamen — Sat, 31 Dec 2022 00:00:00 +0000

In this article, the He’s variation iteration method (VIM) and Elzaki integral transform are proposed to analyze the time-fractional telegraph equations arising in electromagnetics. The Caputo sense is used to describe fractional derivatives. One of the advantages of this technique is that there is neither need to compute the Lagrange multiplier by calculating the integration in recurrence relations or via taking the convolution theorem. Further, to decrease nonlinear computational terms, the Adomian polynomial is identified with the homotopy perturbation method (HPM). The proposed method is applied to some examples of linear and nonlinear fractional telegraph equations. The solutions obtained by the new computational technique indicate that this method is efficient and facilitates the process of solving time fractional differential equations.