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All Journal dCartesian: Jurnal Matematika dan Aplikasi d'Cartesian: Jurnal Matematika dan Aplikasi Indonesian Journal of Intelligence Data Science (IJIDS)
Benny Pinontoan
Sam Ratulangi University
Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Library & Information Science Mathematics

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Crossing Number of Infinite Family of Extension Kochol's Periodic Graphs Aprilia Getroida Tesalonika Saroinsong; Benny Pinontoan; Chriestie E.J.C. Montolalu
d\'Cartesian: Jurnal Matematika dan Aplikasi Vol. 13 No. 1 (2024): Maret 2024
Publisher : Sam Ratulangi University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35799/dc.13.1.2024.52363

Abstract

At this time, technology is developing very quickly and is increasingly sophisticated. This technological development is certainly closely related to the development of computer technology. A computer is able to control a series of electronic devices using an IC chip that can be filled with programs and logic called microprocessor technology. A microprocessor is a digital component of the VLSI (Very Large Scale Integration) type with very high circuit complexity that is capable of carrying out the functions of a CPU (Central Processing Unit). Among many applications, the problem of crossing number very interesting and important because of its application in the optimization of chip are required in a circuit layout of VLSI. Crossing number used to obtain the lower bound on the amount of chip area of VLSI devices like microprocessor and memory chips additionally, crossings in the circuit layout could cause short circuit and therefore worth minimized independent of the chip area consideration. Some graph can be seen as built by small pieces. A principal tool used in construction of crossing-critical graphs are tiles. In the tile concept, tiles can be arranged by gluing one tile to another in a linear or circular fashion. The series of tiles with circular fashion form an infinite graph family. In this way, the intersection number of this family of graphs can be determined. In this research, has been formed an infinite family graphs The graph formed by gluing together many copies of the tile in circular fashion, where the tile consists of identical tile sections. The results obtained show that the graph has 3-crossing-critical of a graph.
Region Coloring in Minahasa Regency Using Sequential Color Algorithm Yevie Ingamita; Nelson Nainggolan; Benny Pinontoan
d\'Cartesian: Jurnal Matematika dan Aplikasi Vol. 8 No. 2 (2019): September 2019
Publisher : Sam Ratulangi University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35799/dc.8.2.2019.23956

Abstract

Graph Theory is one of the mathematical sciences whose application is very wide in human life. One of theory graph application is Map Coloring. This research discusses how to color the map of Minahasa Regency by using the minimum color that possible. The algorithm used to determine the minimum color in coloring the region of Minahasa Regency that is Sequential Color Algorithm. The Sequential Color Algorithm is an algorithm used in coloring a graph with k-color, where k is a positive integer. Based on the results of this research was found that the Sequential Color Algorithm can be used to color the map of Minahasa Regency with the minimum number of colors or chromatic number χ(G) obtained in the coloring of 25 sub-districts on the map of Minahasa Regency are 3 colors (χ(G) = 3).
The Implementation of Bipartite Graph To Minimize Crossing Number Problem of Crossroads in Manado Timboeleng Axellica Nazareth; Chriestie E.J.C Montolalu; Benny Pinontoan
d\'Cartesian: Jurnal Matematika dan Aplikasi Vol. 8 No. 2 (2019): September 2019
Publisher : Sam Ratulangi University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35799/dc.8.2.2019.24240

Abstract

The Implementation Of Bipartite Graph To Minimize Crossing Number Problem Of  Crossroads In Manado. Supervised by BENNY PINONTAN as main supervisor and CHRIESTIE E. J. C. MONTOLALU as co-supervisor. In general, the crossroads are the meeting points of two-way roads from four different places. This causes cross direction at that point. There are various methods that can be used to minimize the crossing number problem crossroad, for example graph theory. The ability of graph theory can later help describe crossroads in Manado into graph, with nodes and lines. In this case, the crossing number problems will solve by bipartite graph. Bipartite graph is a graph that does not have an odd cycle, and can be partitioned into two parts of a set of vertices. Based on results of this research, the appropriate form of the bipartite graph is and  in two different form. First, with an isolated vertex, and second, without isolated vertex. In the case of crossroads, Bipartite graph turns out to be one method that is very suitable and helps determine the crossing number and its solution quickly.
Book Embedding of Infinite Family ((2h+3 2))-Crossing-Critical Graphs for h=1 with Rational Average Degree r∈(3.5,4) Sheren H. Wilar; Benny Pinontoan; Chriestie E.J.C. Montolalu
d\'Cartesian: Jurnal Matematika dan Aplikasi Vol 9, No 2 (2020): September 2020
Publisher : Sam Ratulangi University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35799/dc.9.2.2020.29166

Abstract

A principal tool used in construction of crossing-critical graphs are tiles. In the tile concept, tiles can be arranged by gluing one tile to another in a linear or circular fashion. The series of tiles with circular fashion form an infinite graph family. In this way, the intersection number of this family of graphs can be determined. In this research, has been formed an infinite family graphs Q_((1,s,b) ) (n) with average degree r between 3.5 and 4. The graph formed by gluing together many copies of the tile P_((1,s,b) ) in circular fashion, where the tile P_((1,s,b) ) consist of two identical pieces of tile. And then, the graph embedded into the book to determine the pagenumber that can be formed. When embed graph into book, the vertices are put on a line called the spine and the edges are put on half-planes called the pages. The results obtained show that the graph Q_((1,s,b) ) (n) has 10-crossing-critical and book embedding of graph has 4-page book.
GUI Application to Setup Simple Graph on the Plane using Tkinter of Python Gery Josua Sumual; Benny Pinontoan; Luther A. Latumakulita
d\'Cartesian: Jurnal Matematika dan Aplikasi Vol. 10 No. 1 (2021): Maret 2021
Publisher : Sam Ratulangi University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35799/dc.10.1.2021.32138

Abstract

In graph theory, drawing a simple graph on the plane might result an intersection of pair of edges that is not intended as a vertex called crossing. The least amount of crossing in any simple drawing of a graph is the crossing number of that graph, 𝑐𝑟(𝐺). Given a graph G and an integer 𝐾, the general problem to proof 𝑐𝑟(𝐺) ≤ 𝐾 is an NP-Complete problem, which means, it is likely intractable. One of the way to proof 𝑐𝑟(𝐺) ≤ 𝐾 is by showing the drawing of graph 𝐺 with 𝐾 number of crossing; doing it with a computer application can be much of help. Therefore, the purpose of our research is to create one using Tkinter of Python. The development of the application is feature driven. The developed features are used to find any simple drawing of graphs on the plane. As the result, the application can proof 𝑐𝑟(𝐾_3,3) ≤ 1, 𝑐𝑟(𝐾_6) ≤ 3, and 𝑐𝑟(𝐾𝐺_5,2) ≤ 2.
Crossing Number of Infinite Family of Extension Kochol's Periodic Graphs Aprilia Getroida Tesalonika Saroinsong; Benny Pinontoan; Chriestie E.J.C. Montolalu
d\'Cartesian: Jurnal Matematika dan Aplikasi Vol. 13 No. 1 (2024): Maret 2024
Publisher : Sam Ratulangi University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35799/dc.13.1.2024.52363

Abstract

At this time, technology is developing very quickly and is increasingly sophisticated. This technological development is certainly closely related to the development of computer technology. A computer is able to control a series of electronic devices using an IC chip that can be filled with programs and logic called microprocessor technology. A microprocessor is a digital component of the VLSI (Very Large Scale Integration) type with very high circuit complexity that is capable of carrying out the functions of a CPU (Central Processing Unit). Among many applications, the problem of crossing number very interesting and important because of its application in the optimization of chip are required in a circuit layout of VLSI. Crossing number used to obtain the lower bound on the amount of chip area of VLSI devices like microprocessor and memory chips additionally, crossings in the circuit layout could cause short circuit and therefore worth minimized independent of the chip area consideration. Some graph can be seen as built by small pieces. A principal tool used in construction of crossing-critical graphs are tiles. In the tile concept, tiles can be arranged by gluing one tile to another in a linear or circular fashion. The series of tiles with circular fashion form an infinite graph family. In this way, the intersection number of this family of graphs can be determined. In this research, has been formed an infinite family graphs The graph formed by gluing together many copies of the tile in circular fashion, where the tile consists of identical tile sections. The results obtained show that the graph has 3-crossing-critical of a graph.
E-ARCHIVE DOCUMENT INFORMATION SYSTEM (CASE STUDY OF SMP NEGERI 12 DUMOGA) Tiara Gloriani Siwu; Benny Pinontoan; Rillya Arundaa
Indonesian Journal of Intelligence Data Science Vol 2 No 1 (2023): Volume 2 No. 1 2023
Publisher : Faculty of Mathematics and Natural Sciences Sam Ratulangi University

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

Document archive processing is currently growing fast but has not been maximized as in SMP Negeri 12 Dumoga, where the document archiving process is still carried out conventionally by storing physical files, which are increasing over time and require a large storage area and extra time to search for the required documents. For this reason, with the development of existing technology, school document archiving can be done through a website-based storage system. The purpose of building this system is to facilitate the educational institutions of SMP Negeri 12 Dumoga in storing and searching documents. In addition, it can minimize the loss of school documents when the documents increase more and more and accumulate. The system was built and developed using the prototype system development method, which is carried out in stages starting from communication, quick plan, modeling quick design, construction of prototype, deployment, delivery and feedback. The website-based archive system can display the number of general and important documents stored in the e-archive. This e-archiving system has four menus: General Documents, Important Documents, Categories, and User Pages. This system can make archiving documents easier for administrative staff at SMP Negeri 12 Dumoga. System development can be done by adding features for photo and video archives documenting activities at SMP Negeri 12 Dumoga and development as part of the school's main website.
Co-Authors Aprilia Getroida Tesalonika Saroinsong Chriestie E.J.C Montolalu Chriestie E.J.C. Montolalu Gery Josua Sumual Luther A. Latumakulita Nelson Nainggolan Rillya Arundaa Sheren H. Wilar Tiara Gloriani Siwu Timboeleng Axellica Nazareth Yevie Ingamita