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All Journal dCartesian: Jurnal Matematika dan Aplikasi d'Cartesian: Jurnal Matematika dan Aplikasi
Chriestie E.J.C. Montolalu
Sam Ratulangi University
Computer Science & IT 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.
Penerapan Model SIR Terhadap Perkembangan Penyakit Demam Berdarah Dengue di Kota Tomohon Suhendri A. Londah; Charles E. Mongi; Chriestie E.J.C. Montolalu
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.8.2.2019.24066

Abstract

SUHENDRI ARLANDO LONDAH. Penerapan Model SIR terhadap perkembangan Penyakit Demam Berdarah Dengue (DBD) di Kota Tomohon. Dibawah bimbingan CHRIESTIE MONTOLALU sebagai ketua dan CHARLES MONGI sebagai anggota.Penelitian ini bertujuan untuk menentukan titik kesetimbangan model penyebaran penyakit DBD di Kota Tomohon dalam penerapan model SIR. Data yang digunakan adalah data jumlah penderita DBD dan jumlah penduduk di Kota Tomohon tahun 2015-2017 dari Dinas Kesehatan Daerah dan Badan Pusat Statistik Kota Tomohon. Dari hasil penelitian menunjukkan bahwa terdapat dua titik kesetimbangan model SIR terhadap perkembangan penyakit DBD di Kota Tomohon yaitu titik bebas penyakit dan titik tetap endemik. Nilai bilangan reproduksi dasar penyakit DBD di Kota Tomohon yang ada di lima wilayah kecamatan semuanya . Hasil ini menunjukkan penyakit DBD di Kota Tomohon akan berkurang. Sehingga jumlah penderita DBD akan berkurang dalam kurun waktu tertentu. Kata kunci:   DBD, Model SIR, Bilangan Reproduksi Dasar, Keseimbangan. SUHENDRI ARLANDO LONDAH. The application of the SIR Model to the development of Dengue Fever in Tomohon City. Supervised by CHRIESTIE MONTOLALU as main supervisor and CHARLES MONGI as co-supervisor.This study aims to determine the balance point of the model of the spread of  Dengue Fever in Tomohon City in the application of the SIR model.The data is used on the nnumber of people of Dengue Fever and the number of residents in Tomohon City in 2015-2017 from the Regional Health Official and the Tomohon City Central Bureau of Statistics. The results of the study indicate that there is two equilibrium point of the SIR model for the development of dengue in Tomohon City, which is a disease free equilibrium and endemic equilibrium. The value of basic reproductive numbers of Dengue Fever in Tomohon city in all five sub-districts . These results indicate that dengue in Tomohon City will decrease. So that the number of dengue sufferers will decrease in a certain period of time. Keywords : Dengue Fever, SIR Model, Basic Reproductive Reproductive Number, Equilibrium. 
Optimasi Pengaturan Lampu Lalu Lintas dengan menggunakan Metode Webster (Studi Kasus Persimpangan Jalan Babe Palar) Indah Poernamasari; Rinancy Tumilaar; Chriestie E.J.C. Montolalu
d\'Cartesian: Jurnal Matematika dan Aplikasi Vol. 8 No. 1 (2019): Maret 2019
Publisher : Sam Ratulangi University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35799/dc.8.1.2019.24590

Abstract

A B S T R A K      Permasalahan pada lalu lintas disebabkan karena bertambahnya jumlah kendaraan yang beroperasi setiap harinya sehingga menyebabkan kemacetan parah dibeberapa titik, terutama pada persimpangan jalan yang memiliki lampu lalu lintas dengan nyala lampu merah yang lama dan nyala lampu hijau yang sangat singkat. Permasalahan lampu lalu lintas dapat diselesaikan dengan teori graf. Arus direpresentasikan sebagai titik dan arus yang kompatibel direpresentasikan oleh sisi. Pengoptimalan lampu lalu lintas ditentukan menggunakan metode webster. Dari penelitian yang telah dilakukan diperoleh 3 fase untuk menghitung nyala lampu pada persimpangan jalan Babe Palar dengan waktu siklus optimum yang dihasilkan sebesar 137 detik dan penambahan waktu nyala lampu hijau pada ruas jalan yang memiliki tingkat volume lalu lintas yang tinggi. Sehingga, penghitungan dengan metode webster dikatakan efektif.  
Dijkstra Algorithm for Determining the Shortest Path in the Case of Seven Hotels in Manado City Towards Manado’s Sam Ratulangi Airport. Yohana Permata Hutapea; Chriestie E.J.C. Montolalu; Hanny A.H. Komalig
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.9.2.2020.29146

Abstract

Manado city has many notable tourist sites, resulting in the increase of the number of tourists visiting every year. Tourists require hotels with adequate facilities for their stay, such as 4-star hotels. After visiting Manado, tourists go back to where they come from. One of the transportation mode being used is airplanes. They then need a path to go through and not the usual one; they need the shortest path to get to Sam Ratulangi airport. Based on previous research, the shortest path is modeled by Graph Theory. Hotels will be represented as vertices, and the path from each hotels and to the airport will be represented as edges. The shortest path are searched by using Dijkstra’s Algorithm then will see the difference to shortest path from google maps. Based on the analysis results, Dijkstra’s Algorithm selects the shortest path with the smallest weight. The difference between Dijkstra’s Algorithm and google maps can be concluded that, in determining the shortest path used for the trip from the 4-star hotel to the airport, Dijkstra’s Algorithm is emphasized towards short travel distance, whereas google maps is emphasized more in short travel time.
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.
Sistem Pendukung Keputusan untuk Penentuan Tingkat Kerawanan Kamtibmas menggunakan Metode Simple Additive Weighting Villy Setiono; Altien J. Rindengan; 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.9.2.2020.29555

Abstract

Keamanan dan ketertiban masyarakat (kamtibmas) menjadi poin penting dalam terselenggaranya pembangunan nasional. Namun kerawanan kamtibmas belakangan ini menyebabkan terhambatnya pembangunan nasional ini. Sehingga perlu tindakan untuk mengurangi kerawanan kamtibmas ini, khususnya oleh pihak Kepolisian Republik Negara Indonesia (Polri) yang merupakan alat utama negara untuk memelihara kamtibmas. Penelitian ini bertujuan untuk membuat suatu Sistem Pendukung Keputusan (SPK) yang menerapkan metode Simple Additive Weighting (SAW) untuk menentukan tingkat kerawanan kamtibmas dari wilayah tingkat Polsek di Polres Minahasa. Dengan menggunakan 10 Polsek sebagai atribut, 18 data pendukung untuk kriteria, serta bobot kriteria yang diperoleh dari pengambilan data sekunder di Polres Minahasa. Berdasarkan pengujian sistem diperoleh hasil bahwa sistem yang dibuat mampu menerapkan metode SAW dengan baik dan memeringkatkan 10 Polsek berdasarkan tingkat kerawanannya. Sistem memeringkatkan 10 Polsek tersebut secara berurut berdasar tingkat kerawanan tertinggi yaitu Polsek Tondano, Polsek Toulimambot, Polsek Eris, Polsek Kakas, Polsek Tompaso, Polsek Remboken, Polsek Langowan, Polsek Lembean Timur, Polsek Kombi dan Polsek Kawangkoan.
Lintasan Hamiltonian pada Graf 4-Connected Roy Andreas Melville Makalew; Chriestie E.J.C. Montolalu; Mans L. Mananohas
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.9.2.2020.29735

Abstract

Teori graf merupakan salah satu materi dalam ilmu Matematika yang digunakan dalam bentuk representasi masalah secara deskripsi. Menurut beberapa penelitian,teori graf banyak digunakan untuk menganalisa topik yang berkaitan dengan transpotasi, rangkaian jaringan komputer atau telepon, dan hal lainnya. Tujuan penelitian ini , yaitu untuk membuktikan bahwa penggunaan 4-connected graph yang dibentuk dari beberapa definisi graf telah didapatkan model graf 4-connected graph yang tidak Uniquely Hamiltonian.. Penelitian ini dilakukan dengan menggunakan sumber pustaka dan sumber jurnal terpercaya. Dengan batasan graf yang digunakan yaitu graf sederhana, graf terhubung dan graf Hamilton. Dari hasil dapat diketahui bahwa model graf G yang di dapat ,yaitu graf lengkap  memenuhi batasan graf dan definisi ­­­4-connected. Sehingga disimpulkan sebagai graf ­­­4-connected bukanlah graf Uniquely Hamiltonian.
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.
Co-Authors Altien J. Rindengan Aprilia Getroida Tesalonika Saroinsong Benny Pinontoan Charles E. Mongi Hanny A.H. Komalig Indah Poernamasari Mans L. Mananohas Roy Andreas Melville Makalew Sheren H. Wilar Suhendri A. Londah Tumilaar, Rinancy Villy Setiono Yohana Permata Hutapea