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All Journal Elkom: Jurnal Elektronika dan Komputer Limits: Journal of Mathematics and Its Applications
Kurniawan Atmadja
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Computer Science & IT Education Mathematics

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Pelabelan Harmonis pada Graf Tangga Segi Tiga Paku Kurniawan Atmadja; Miftahul Fikri
Limits: Journal of Mathematics and Its Applications Vol. 20 No. 2 (2023): Limits: Journal of Mathematics and Its Applications Volume 20 Nomor 2 Edisi Ju
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

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Abstract

Graf dapat ditulis , yaitu himpunan tak kosong simpul ( vertex ) dan himpunan sisi ( edge ) Pada graf diketahui jumlah simpul dan jumlah sisi yang masing - masing dinotasikan dengan dan Graf yang diberi label harmonis selalu mensyaratkan jumlah simpul tidak melebihi jumlah sisi. Pelabelan harmonis adalah fungsi injektif dari himpunan simpul ke himpunan bilangan bulat modulo yang membangkitkan fungsi bijektif dari himpunan sisi ke himpunan bilangan bulat modulo dengan yang menghasilkan label sisi yang berbeda. Kajian penelitian ini bertujuan untuk menambah koleksi graf harmonis dalam bidang Matematika kombinatorik, khususnya berkaitan dengan penelitian graf tangga segitiga paku yang berkelanjutan. Graf tangga segitiga paku diperoleh dari hasil graf tangga segitiga yang mengalami tambahan satu simpul dan dua sisi. Kemudian dikonstruksi menyusun dan berbaris, sehingga mendapatkan hasil sebuah graf baru yang berbentuk seperti paku yang bersusun, terhubung dan berbaris. Lalu diberi label pada simpul dan sisi. Telah diketahui bahwa graf tangga segitiga adalah graf harmonis. Pada paper ini ditunjukan bahwa graf tangga segitiga paku juga merupakan graf harmonis.
Kerangka Hibrida Apriori–MST untuk Mengungkap Struktur Dasar Pola Pembelian Konsumen Marta Dinata, Riadi; Kurniawan Atmadja; Marhaeni Mahaeni; Lely Mustika
Elkom: Jurnal Elektronika dan Komputer Vol. 18 No. 2 (2025): Desember : Jurnal Elektronika dan Komputer
Publisher : STEKOM PRESS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.51903/elkom.v18i2.3300

Abstract

Traditional association rule analysis is effective at uncovering co-purchase patterns but fails to provide a global structural view of the market, which often results in fragmented and isolated insights. This study proposes a hybrid framework that integrates the Apriori algorithm with a Minimum Spanning Tree (MST) in order to validate and contextualize association rules within a single structural backbone. Transaction data from a retail store are transformed into a weighted, undirected product graph using an inverse-support function, and an MST is then extracted to represent the market backbone, while frequent itemsets and strong rules are obtained using Apriori. Experimental results on 236 multi-item transactions show that the MST backbone comprises 10 products and 9 fundamental links, with 66.67% of these links being confirmed by strong association rules, indicating a substantial coherence between statistical and structural evidence. The proposed model identifies 41 Apriori patterns that can be embedded in the MST and ranks them using a new metric, Structural Distance, which enables the categorization of Core Patterns, Bridge Patterns, and Complex Patterns according to their structural tightness. This hybrid perspective distinguishes dense, strategically meaningful bundles from anomalous but frequent combinations that are structurally peripheral, thereby offering a more holistic and actionable alternative to conventional Market Basket Analysis. The validated framework can support various applications, including store layout optimization, cross-selling strategies, and the design of path-based recommender systems, and it opens avenues for future extensions based on dynamic graphs and Graph Neural Networks.
Co-Authors Marhaeni Mahaeni Marta Dinata, Riadi Miftahul Fikri Mustika, Lely