Pewarnaan Pelangi pada Graf Garis dari Graf Ilalang (S_(3,r))

  • Dewi Nur Angriani Rauf Universitas Negeri Gorontalo
  • Novianita Achmad Universitas Negeri Gorontalo
  • Nisky Imansyah Yahya Universitas Negeri Gorontalo
Keywords: rainbow connection, line graph, ilalang graph

Abstract

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.

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Published
2025-03-28
Section
Articles