Bilangan Rainbow Connection pada Graf Siput dan Graf Ubur-Ubur

Gema Hista Medika (Departemen Matematika Dan Sains Data, Fakultas Matematika dan Ilmu Pengetahuan Alam, Universitas Andalas, Padang)
Syafrizal Sy (Departemen Matematika Dan Sains Data, Fakultas Matematika dan Ilmu Pengetahuan Alam, Universitas Andalas, Padang)
Muhafzan (Departemen Matematika Dan Sains Data, Fakultas Matematika dan Ilmu Pengetahuan Alam, Universitas Andalas, Padang)
Zulfaneti (Universitas PGRI Sumatera Barat, Padang)

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

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.