KETERHUBUNGAN PELANGI KUAT (src) PADA GRAF (1 Spl-(Cn )) UNTUK 3 ≤ n ≤ 10

  • Ermita Rizki Albirri Universitas Jember
  • Robiatul Adawiyah Universitas Jember
  • Lela Nur Safrida Universitas Jember
  • Reza Ambarwati Universitas Jember
Keywords: strong rainbow connection number, split graph, 1 Spl - (Cn) Graph

Abstract

Let G be nontrivial and connected graph. A total-coloured path is called as total-rainbow if its edges and internal vertices have distinct colours. For any two vertices u and v of G, a rainbow u−v geodesic in G is a rainbow u−v path of length d(u,v), where d(u,v) is the distance between u and v. The graph G is strongly rainbow connected if there exists a rainbow u−v geodesic for any two vertices u and v in G. The strong rainbow connection number of G, denoted src(G), is the minimum number of colors that are needed in order to make G strong rainbow connected. The result shows for  1 Spl - (Cn) and 3 ≥ n ≥ 10 there exist a coloring where diam(G) = rc(G) = src(G) ≤ m and diam(G) ≤ rc(G) ≤ src(G) ≤ m with m is the number of path 1 Spl - (Cn).

 

References

[1] Chartrand, G., dkk. 2008. Rainbow Connection in Graphs. Mathematica Bohemica. 133 : 85-98.
[2] Kiki, A. S., dkk. 2014. Teori Graf dan Aplikasinya. Departemen Matematika FMIPA Universitas Indonesia. Jakarta.
[3] Vaidya, S. K., dkk. Some New Odd Harmonious Graphs. International Journal of mathematics and soft Computing. 1 : 9-16.
Published
2018-06-01