RAINBOW CONNECTION NUMBER AND TOTAL RAINBOW CONNECTION NUMBER OF AMALGAMATION RESULTS DIAMOND GRAPH(〖Br〗_4) AND FAN GRAPH(F_3)

  • Sumarno Ismail Mathematics Department, Faculty of Mathematics and Natural Sciences, Universitas Negeri Gorontalo
  • Isran K. Hasan Mathematics Department, Faculty of Mathematics and Natural Sciences, Universitas Negeri Gorontalo
  • Tesya Sigar Mathematics Department, Faculty of Mathematics and Natural Sciences, Universitas Negeri Gorontalo
  • Salmun K. Nasib Mathematics Department, Faculty of Mathematics and Natural Sciences, Universitas Negeri Gorontalo
DOI: https://doi.org/10.30598/barekengvol16iss1pp023-030
Keywords: diamond graph, fan graph, amalgamation operation, rainbow connection numbers

Abstract

If be a graph and edge coloring of G is a function , rainbow connection number is the minimum-k coloration of the rainbow on the edge of graph G and denoted by rc(G). Rainbow connection numbers can be applied to the result of operations on some special graphs, such as diamond graphs and fan graphs. Graph operation is a method used to obtain a new graph by combining two graphs. This study performed amalgamation operations to obtain rainbow connection numbers and rainbow-total-connection numbers in diamond graphs ( ) and fan graphs ( ) or . Based on the research, it is obtained that the rainbow-connection number theorem on the amalgamation result of the diamond graph ( ) and fan graph (  is  with . Furthermore, the theorem related to the total rainbow-connection number on the amalgamation result of the diamond graph( ) and the fan graph (  is obtained, namely  with .

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Published
2022-03-21
How to Cite
[1]
S. Ismail, I. Hasan, T. Sigar, and S. Nasib, “RAINBOW CONNECTION NUMBER AND TOTAL RAINBOW CONNECTION NUMBER OF AMALGAMATION RESULTS DIAMOND GRAPH(〖Br〗_4) AND FAN GRAPH(F_3)”, BAREKENG: J. Math. & App., vol. 16, no. 1, pp. 023-030, Mar. 2022.
Issue
Vol 16 No 1 (2022): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Section
Articles

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