Pewarnaan Pelangi pada Graf Garis dari Graf Ilalang (S_(3,r)) - Rauf, Dewi Nur Angriani; Achmad, Novianita; Yahya, Nisky Imansyah (Griya Journal of Mathematics Education and Application, 2025)
The rainbow connection number, denoted by rc(G), is the minimum number of colors required to color the edges of a graph G such that the graph is rainbow connected. A graph G is said to be rainbow connected if every pair of vertices in the graph has at least one rainbow path, a path in which each edge has a different color. Rainbow coloring has been extensively studied on various types of graphs and their modifications, including line graphs. The line graph L(G) of a graph is a graph whose vertex set is V(L(G)) = E(G), meaning each vertex in represents an edge of . Two vertices in L(G) are adjacent if and only if their corresponding edges in G share a common vertex. This study examines the rainbow coloring of the line graph of the ilalang graph (Sn,r) for n = 3 and r>= 3. Based on the research findings, the rainbow connection number of the line graph of the ilalang graph is given by the theorem rc(L(S3,r)) = r for r>= 3.