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All Journal EKSAKTA: Journal of Sciences and Data Analysis BAREKENG: Jurnal Ilmu Matematika dan Terapan
Rian Kurnia
Mathematics Department, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Indonesia
Chemical Engineering, Chemistry & Bioengineering Chemistry Computer Science & IT Control & Systems Engineering Earth & Planetary Sciences Economics, Econometrics & Finance Energy Engineering Materials Science & Nanotechnology Mathematics Mechanical Engineering Physics Transportation

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ON PROPERTIES OF PRIME IDEAL GRAPHS OF COMMUTATIVE RINGS Kurnia, Rian; Abrar, Ahmad Muchlas; Syarifudin, Abdul Gazir; Wijaya, Verrel Rievaldo; Supu, Nur Ain; Suwastika, Erma
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 17 No 3 (2023): BAREKENG: Journal of Mathematics and Its Applications
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol17iss3pp1463-1472

Abstract

The prime ideal graph of in a finite commutative ring with unity, denoted by , is a graph with elements of as its vertices and two elements in are adjacent if their product is in . In this paper, we explore some interesting properties of . We determined some properties of such as radius, diameter, degree of vertex, girth, clique number, chromatic number, independence number, and domination number. In addition to these properties, we study dimensions of prime ideal graphs, including metric dimension, local metric dimension, and partition dimension; furthermore, we examined topological indices such as atom bond connectivity index, Balaban index, Szeged index, and edge-Szeged index.
Optimizing Medan Tourist Routes Using BiogeographyBased Optimization Zai, Fidelis Nofertinus; Nainggolan, Donni Andreas; Kurnia, Rian; -, Erwin
EKSAKTA: Journal of Sciences and Data Analysis VOLUME 7, ISSUE 1, April 2026
Publisher : Fakultas Matematika dan Ilmu Pengetahuan Alam

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20885/EKSAKTA.vol7.iss1.art8

Abstract

This study optimizes tourist routes across 14 destinations in the city of Medan using the Biogeography-Based Optimization (BBO) algorithm. The problem is formulated as a closed-path Traveling Salesman Problem (TSP) with an extension allowing for flexibility in freely selecting the starting point. The route is determined based on the distance between two locations, where the distance is assumed to be asymmetric to account for real-world urban road conditions such as one-way systems, while ignoring traffic conditions and other costs. Simulation results show that even though the starting point is freely determined, the BBO algorithm is still able to consistently produce routes that are close to optimal with stable convergence. The main contribution of this study is the provision of an adaptive and realistic route planning model to support tourism information systems in urban areas.
Co-Authors Abrar, Ahmad Muchlas Erwin - Nainggolan, Donni Andreas Supu, Nur Ain Suwastika, Erma Wijaya, Verrel Rievaldo ZAI, FIDELIS NOFERTINUS