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Bilangan Rainbow Connection pada Graf Siput dan Graf Ubur-Ubur Gema Hista Medika; Syafrizal Sy; Muhafzan; Zulfaneti
Limits: Journal of Mathematics and Its Applications Vol. 23 No. 2 (2026): Limits: Journal of Mathematics and Its Applications Volume 23 Nomor 2 Edisi Ju
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/limits.v23i2.9561

Abstract

The rainbow connection number is a topic in graph theory that studies the minimum number of colors required on the edges of a graph such that every pair of vertices is connected by a path with distinct edge colors. This study aims to determine the rainbow connection number of snail graphs and jellyfish graphs. The method used is a theoretical approach through structural analysis of graphs and the construction of minimum edge-coloring patterns that satisfy the rainbow connected property. The results show that the rainbow connection number of the snail graph Sl_n is rc(Sl_n)=4 for n=1,2, rc(Sl_n)=5 for n=3,4, and rc(Sl_n)=6 for n≥5. Meanwhile, for the jellyfish graph J_n, it is obtained that rc(J_n)=2n+1. These results indicate that the structure of a graph significantly influences the rainbow connection number. Although the diameter of the jellyfish graph is constant, the structural complexity causes the rainbow connection number to increase linearly with respect to n. This study is expected to contribute to the development of research on rainbow connection in special graphs.
Impact of Speckle Reduction Filters on Machine Learning-Based Detection of Polycystic Ovary Syndrome from Ovarian Ultrasound Images Fazrol Rozi; Syafrizal Sy; Adiwijaya; Yusrawati; Primawati
Jurnal RESTI (Rekayasa Sistem dan Teknologi Informasi) Vol 10 No 4 (2026): August 2026
Publisher : Ikatan Ahli Informatika Indonesia (IAII)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29207/resti.v10i4.7658

Abstract

Polycystic Ovary Syndrome (PCOS) is commonly assessed with ovarian ultrasonography, but speckle can conceal follicular margins and reduce the robustness of automated interpretation. Although automated PCOS studies increasingly employ machine learning, the contribution of conventional despeckling to subsequent segmentation and classification has not been examined consistently. This study compares five classical filters - Mean, Median, Lee, Frost, and Kuan - within an interpretable machine-learning pipeline for ovarian ultrasound analysis. From a public collection of 12,680 images, a balanced sample of 300 scans (150 PCOS and 150 non-PCOS) was selected. Two radiologists produced follicle annotations, and disagreements were resolved with a third expert to obtain consensus masks. Each filtered image was segmented by adaptive thresholding with morphological refinement, after which geometric and intensity descriptors were extracted. Support Vector Machine (SVM), Random Forest (RF), k-Nearest Neighbors (k-NN), and Logistic Regression (LR) were trained using a stratified 70/30 train-test split with cross-validated hyperparameter tuning. The Kuan-LR configuration yielded the strongest result, reaching 94.44% accuracy and an AUC of 0.98, together with the best edge-preservation score and segmentation agreement. The results indicate that preprocessing materially affects the reliability of an interpretable PCOS detection pipeline and provide quantitative guidance for selecting a speckle-reduction strategy before segmentation and classification.