Bilangan Terhubung Pelangi pada Graf Tengah (M(G)) dari Graf Ulat (C_(m,2))

Authors

  • Fuji Fauzia Kiayi Program Studi Matematika, Universitas Negeri Gorontalo, Bone Bolango 96554, Indonesia
  • Sumarno Ismail Program Studi Pendidikan Matematika, Universitas Negeri Gorontalo, Bone Bolango 96554, Indonesia
  • Nisky Imansyah Yahya Program Studi Matematika, Universitas Negeri Gorontalo, Bone Bolango 96554, Indonesia
  • Lailany Yahya Program Studi Matematika, Universitas Negeri Gorontalo, Bone Bolango 96554, Indonesia
  • Salmun K. Nasib Program Studi Statistika, Universitas Negeri Gorontalo, Bone Bolango 96554, Indonesia

DOI:

https://doi.org/10.55657/rmns.v4i1.204

Keywords:

Rainbow Connection Number, Middle Graph, Caterpillar Graph

Abstract

Edge coloring of a graph  is considered rainbow connected if the graph is connected and a rainbow path exists for every pair of points. The rainbow connection number of a graph, denoted as , represents the smallest number of colors required to make the graph is rainbow connected. This study examines the rainbow connection number of the middle graph  of a caterpillar graph. The middle graph is a modified result of a graph , denoted as . It is described as a graph constructed from the intersection of a set of points and edges. The set of points in the middle graph  consists of the combination of points and edges of the graph . Two points are considered adjacent if only they are connected in , or if one point corresponds to a point and the other corresponds to an edge adjacent to it. A caterpillar graph denoted by   is a tree that will be a path if all the leaf points are deleted. The results of this research show the rainbow-connected number theorem for the middle graph of the caterpillar graph  for .

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Published

22-02-2025

How to Cite

[1]
F. F. Kiayi, S. Ismail, N. I. Yahya, L. Yahya, and S. K. Nasib, “Bilangan Terhubung Pelangi pada Graf Tengah (M(G)) dari Graf Ulat (C_(m,2))”, Res. Math. Nat. Sci., vol. 4, no. 1, pp. 65–73, Feb. 2025.

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