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All Journal d'Cartesian: Jurnal Matematika dan Aplikasi
Chriestie E.J.C. Montolalu
Universitas Sam Ratulangi
Mathematics

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Derajat Laplacian dari Graf Lengkap, Graf Bipartisi Komplit, Graf Matahari dan Graf yang memiliki n-1 Derajat berbeda Yohanes Imanuel Runtunuwu; Mans L. Mananohas; Chriestie E.J.C. Montolalu
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.10.1.2021.32698

Abstract

Graf didefinisikan sebagai pasangan himpunan , yang dalam hal ini  adalah himpunan simpul-simpul (vertices) dan  adalah himpunan sisi (edges). Perkembangan dari Teori Graf dapat dihubungkan dengan cabang ilmu Matematika yang lain seperti Aljabar yang menarik untuk dibahas. Sebuah graf dapat direpresentasikan ke dalam Matriks Laplacian (pengurangan matriks derajat dan matriks ketetanggaan) yang dapat dihitung nilai eigennya. Tujuan penelitian ini adalah untuk membuktikan pada graf terhubung (connected graph) pertidaksamaan , bilangan  adalah derajat Laplacian terbesar ke- pada matriks Laplacian,  merupakan nilai Eigen terbesar ke-  pada matriks Laplacian dan  merupakan derajat terbesar ke-  dari graf terhubung  sehingga berlaku untuk . Penelitian ini dilakukan menggunakan studi pustaka. Hasil penelitian diketahui bahwa  berlaku untuk  pada batasan graf terhubung.  
Single Index Model in Forming the Optimal Portfolio Before and During the Covid-19 Pandemic on LQ-45 Shares. Vita Indriani Wahyuningsih; Chriestie E.J.C. Montolalu; Tohap Manurung
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.10.1.2021.32979

Abstract

Investment is a commitment to place a number of funds in an asset to gain benefits in the future. but there will be unexpected risks in investment such as the covid-19 pandemic. a strategy to minimize the risk is to form a portfolio. This study aims to form an optimal portfolio before and during the covid-19 pandemic on LQ-45 shares along with the proportion of funds for each share obtained using a single index model. The data used are in the form of daily stock closing prices, JCI price, and risk-free interest rates. The results of this research get a combination of six stocks and the proportion of funds for data before covid-19 are BTPS gets 15.61%, MNCN gets 6.69%, EXCL gets 19.89%, CTRA gets 9.81%, ICBP gets 10.62%, BBCA gets 37.38% and four stocks combination and the proportion of funds for data during covid-19 are INCO gets 30.09%, ANTM gets 27.54%, INKP gets 22.81%, KLBF gets 19.56%. INCO, ANTM, INKP, KLBF shares can be considered by investors in making investment decisions during the covid-19 pandemic.
EKSENTRISITAS DIGRAF PADA GRAF GIR MENGGUNAKAN ALGORITMA BREADTH FIRST SEARCH Romario Marselino Barahama; Chriestie E.J.C. Montolalu; Rinancy Tumilaar
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.10.1.2021.32995

Abstract

Let  be a graph with the set of points  and the set of sides . The distance from point u to v in  is the length of shortest path from point  to , denoted by . The eccentricity of point  in graph  is the furthest distance from point to each in  denoted by . The point  is the eccentic point of  if . The purpose of this research is determine the eccentricity of the digraph on the gear graph  and determine the eccentricity of the digraph  gear graph using the breadth first search algorithm. The method used is to collect library sources in the form of books other refrences ehich are then used as the basis for conducting this research. Based on the discussion it can be concluded that the sahpe of eccentricity of the digraph on graph  is complete symetry with Graph Theory is the one of the math theory with mathematic knowledge using with ,  and , while for the eccentricity the digraph on the digraph gear  uses  breadth first search algorithm is ,  and .
Co-Authors Mans L. Mananohas Romario Marselino Barahama Tohap Manurung Tumilaar, Rinancy Vita Indriani Wahyuningsih Yohanes Imanuel Runtunuwu