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All Journal International Journal of Electrical and Computer Engineering Journal of the Indonesian Mathematical Society Sinkron : Jurnal dan Penelitian Teknik Informatika Building of Informatics, Technology and Science MES: Journal of Mathematics Education and Science Journal of Research in Mathematics Trends and Technology Journal of Applied Data Sciences
Saib Suwilo
Department of Mathematics, University of Sumatera Utara
Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Electrical & Electronics Engineering Mathematics

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PENENTUAN BILANGAN KROMATIK HARMONIK PADA GRAF HASIL KALI KARTESIAN ANTARA GRAF LINTASAN DENGAN TIGA TITIK DAN GRAF BINTANG DENGAN (N+1) TITIK Feren, Feren; Suwilo, Saib; Mardiningsih, Mardiningsih; Yanti, Maulida
MES: Journal of Mathematics Education and Science Vol 11, No 1 (2025): Edisi Oktober
Publisher : Universitas Islam Sumatera Utara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30743/mes.v11i1.11405

Abstract

This research discusses the harmonious chromatic number on the Cartesian product of a path graph with three vertices (P_3) and a star graph with n vertices (S_n). Harmonious coloring is a vertex coloring of a graph such that each pair of colors appears on at most one edge. The objective of this research is to develop a harmonious coloring algorithm and also to determine and prove a general formula for the harmonious chromatic number of the graph P_3×S_n. The research method is literature-based with a mathematical approach, start from constructing modified adjacency matrices until testing the coloring algorithm. The proof is conducted through mathematical induction and structural graph analysis. The result shows that the harmonious chromatic number of P_3×S_n for n=1 is 5, for n=2,3 is 7, for n=4 is 8, whereas for n≥5, it is n+3.
Co-Authors Aghni Syahmarani Aghni Syahmarani Ahmad Zaki Mubarak, Ahmad Zaki Christy, Claudia Efendi, Syahril Elly Rosmaini Erna Budhiarti Nababan Feren, Feren Gayus Simarmata, Gayus Harahap, Desti Alannora Hasibuan, Shubuhan Syukri Herman Mawengkang Mardiansyah, Heru Mardiningsih Mardiningsih , Mardiningsih Mardiningsih Mardiningsih Muhammad Zarlis, Muhammad Nasution, Putri Khairiah Opim Salim Sitompul Pasaribu, Suhendri Prandana, Randy Pujiana, Perli Pulungan, Annisa Fadhillah Putri, Mimmy Sari Syah Rezeki, Ema Sri Riansyah, Muhammad Rizka Fitria, Rizka Rumahorbo, Yuli Sukiman, T. Sukma Achriadi Sutarman Sutarman Tarigan, Aam Jon Mintase Tarigan, Ruffiana Tulus Tulus Yanti, Maulida