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

Authors

  • Ermita Rizki Albirri Universitas Jember
  • Robiatul Adawiyah Universitas Jember
  • Lela Nur Safrida Universitas Jember
  • Reza Ambarwati Universitas Jember

DOI:

https://doi.org/10.52166/ujmc.v4i1.844

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.

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Published

2018-06-01

How to Cite

Albirri, E. R., Adawiyah, R., Safrida, L. N., & Ambarwati, R. (2018). KETERHUBUNGAN PELANGI KUAT (src) PADA GRAF (1 Spl-(Cn )) UNTUK 3 ≤ n ≤ 10. UJMC (Unisda Journal of Mathematics and Computer Science), 4(1), 39–48. https://doi.org/10.52166/ujmc.v4i1.844

Issue

Vol. 4 No. 1 (2018): Unisda Journal of Mathematics and Computer Science

Section

Articles

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