Total Rainbow Connection Number of Corona Product of Book Graph(Bn) and Pencil Graf(Pcm)

Randi Mooduto(1*), Lailany Yahya(2), Nisky Imansyah Yahya(3),

(1) Program Studi Matematika, Jurusan Matematika, Fakultas Matematika dan Ilmu Pengetahuan Alam, Universitas Negeri Gorontalo
(2) Program Studi Matematika, Jurusan Matematika, Fakultas Matematika dan Ilmu Pengetahuan Alam, Universitas Negeri Gorontalo
(3) Program Studi Matematika, Jurusan Matematika, Fakultas Matematika dan Ilmu Pengetahuan Alam, Universitas Negeri Gorontalo
(*) Corresponding Author




DOI: https://doi.org/10.35580/sainsmat122423112023

Abstract


Let G be a simple and finite graph. Rainbow connection and total rainbow connection c are set c : G → {1,2,. . . , k} where k is the minimal color on graph G. A rainbow connection number(rc) is a pattern by giving different colors to the connection edges (E(G)) so that a rainbow path is formed. The total rainbow connection number (trc) is a payment pattern by giving color to vertices (V(G)) and edges (E(G)) in graph G so that a total rainbow path is formed. This article discusses rainbow connection numbers (rc) and total rainbow connection numbers (trc) in the corona graph of book graph (Bn) and pencil graph (Pcm). The results obtained are rc(Bn ⨀ Pcm) = 2n+3 and trc(Bn ⨀ Pcm) = 4n+5, 3 ≤ n ≤ 5.

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