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All Journal Pendidikan Matematika Jurnal Pelangi LEMMA: Letters Of Mathematics Education Math Educa Journal Jurnal Matematika UNAND LEBAH Smart Dedication: Jurnal Pengabdian Masyarakat
Zulfaneti Zulfaneti
Universitas PGRI Sumatera Barat
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RAINBOW CONNECTION NUMBERS IN GRAPHS: A COMPREHENSIVE STUDY Gema Hista Medika; Syafrizal Sy; Muhafzan Muhafzan; Zulfaneti Zulfaneti
Math Educa Journal Vol 10, No 1 (2026)
Publisher : UIN Imam Bonjol Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15548/mej.v10i1.13681

Abstract

The rainbow connection number is a graph parameter that integrates edge colouring and graph connectivity. A connected graph is said to be rainbow connected if every pair of vertices is joined by a path whose edges have distinct colours, and the rainbow connection number represents the minimum number of colours required to satisfy this property. This study aims to provide a comprehensive and systematic analysis of research developments related to rainbow connection numbers in graphs. The method employed is a systematic literature review of reputable international journals and nationally accredited publications. The analysis covers fundamental definitions, known values for various classes of graphs, relationships with structural parameters such as diameter, minimum degree, and connectivity, as well as computational complexity and several important variants, including strong rainbow connection, rainbow vertex-connection, and total rainbow connection. The results indicate that the rainbow connection number is strongly influenced by graph structure, with diameter serving as a natural lower bound and connectivity contributing to tighter upper bounds. Furthermore, determining the exact value for general graphs is computationally intractable, motivating the use of approximation and heuristic approaches. This study also identifies research gaps, particularly in algorithmic development and the analysis of complex graph class, and highlights potential applications in communication networks and network security.
Co-Authors ADRIANI ADRIANI Agusti Nopi Andriani Ahmad Sanusi Ainil Mardiyah Alfadhli Alfadhli Alfi Yunita Anna Cesaria Anny Sovia Ari Limay Trisno Putra Arnes Fitriani Arsu helda Dewi Febriani Dewi Maharani, Ade Dewi Yuliana Fitri Edy Tri Baskoro Elwing Bisefni Erismar Amri Ezi Yolfitra Yeni Fatma Laswita Febrian, Rizky Fevi Oktarani Fitri i Kumala Dewi Gema Hista Medika Heru Marhen Hikmah Fujianti Hilda Assiyatun, Hilda Husna Husna Hutri Melvasari Iga Silviana Ira Afriani Irene Rembaji Irmayenti Irmayenti Jefri Haverdi Lili Vera Rianti Lita Lovia Marta Dewita Mastuti ovtaleny Melisa Melisa Merry Wulandari Miftahul Rahmah Mochammad Imron Awalludin Muhafzan Muhafzan Mukhni Mukhni Mulia Suryani Nelvirina Nelvirina Nices Maryuliasti Nilawasti Nilawasti Nilawasti ZA Nova Priyanti Putri, Asti Ananda Amelia Rafni Dian Putri Rahimullaily Rahimullaily Rahmi Rahmi Rahmil Rahmil Ramadhani Ramadhani Rian febriana Rina Febriana Rini Sulastri Riri Permata Sari Riva Novriani Roza Beti Samudra, Ami Anggraini Sari Wahyuni Sauci Yucarini Sefna Rismen Septia Vramita Fahmi Septian P uspita Sari Sevya Manda Sari Silvia Irani Silvia Ningsih Siska Mulia Syahri Sofia Edriati Steffiyo Steffiyo Syafrizal Sy SYAHRIAL SYAHRIAL Syamsiar, Syamsiar Trisna Julia M Vera Yolanda Sari Viro Handoko Vivien Almira Yelvina Listika Yernita Sulastri Yesmira Syamra, Yesmira Yulia Haryono Yulisa Fitri Yulyanti Harisman Zahra, Salwa Zita Putri Netris