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All Journal Epsilon: Jurnal Matematika Murni dan Terapan Mathematics and Applications (MAp) Journal
Saman Abdurrahman
Lambung Mangkurat University
Decision Sciences, Operations Research & Management Mathematics Transportation

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EDGE COLORING CYCLE BOOKS GRAPH B_(C_n,m) Yeni Rahma Oktaviani; Saman Abdurrahman
MAp (Mathematics and Applications) Journal Vol 8, No 1 (2026)
Publisher : Universitas Islam Negeri Imam Bonjol Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15548/map.v8i1.13832

Abstract

This study investigates the edge coloring of the cycle book graphs, denoted as B_(C_n,m), which consist of m cycles C_n intersection at a shared P_2 path. The primary objective is to identify the chromatic index-the fewest colors needed to ensure no two adjacent edges share the same color. Utilizing a deductive approach, the researchers developed an edge coloring function based on cyclic patterns for both even and odd values of n. The findings establish that the chromatic index χ' (B_(C_n,m) )= m+1 for all n≥3 and m≥2. This result is validated by coloring construction that aligns with the lower bound established by Vizing’s Theorem
ANALISIS KOMPARATIF METODE DES HOLT’S DAN ARIMA TERHADAP PERAMALAN TINGKAT PENGANGGURAN DI PROVINSI KALIMANTAN SELATAN Yeni Rahma Oktaviani; Yalela Sa'adah; Syahputra Wibowo; Saman Abdurrahman
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 19, No 2 (2025)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v19i2.17155

Abstract

Unemployment is crucial issue in South Kalimantan Province as it contribute to increased poverty and the slowing down of regional economic growth. Therefore, reliable forecasting method is needed to support the government in formulating strategic policies. This study aims to compare and identify a representative time series forecasting model for the TPT in South Kalimantan Province. This research compares the performance of the DES Holt 1-parameter, 2 parameter, and ARIMA (1,1,0) models using 19 years of semi-annual unemployment rate data (2005-2024). The models applied parameter optimization for  and , obtained by trial and error and by using R Studio, while accuracy was evaluated using MAPE. The research results show that the DES Holt-2parameter model with optimal parameters  and . Demonstrated better statistical performance compared to the DES Holt 1-parameter and ARIMA (1,1,0) models because it yielded the smallest MAPE error value of 4,66. However, the ARIMA (1,1,0) models is superior because it is more capable of capturing dynamic trend changes in the region, whether the changes are short-term of long-lasting, and can better reflect socioeconomic structural changes. The contribution of this research is to provide a scientific basis and a more superior and representative forecasting model, namely ARIMA (1,1,0), for the South Kalimantan Provincial government in formulating policies for job creation, improving labor productivity, and strengthening the regional economy in a sustainable manner.
Co-Authors Syahputra Wibowo Yalela Sa'adah Yeni Rahma Oktaviani Yeni Rahma Oktaviani