Rainbow Connection and Strong Rainbow Connection Number of Grid 3D Graph
R I Kasih, D R Silaban*, and K A Sugeng
Departemen Matematika, Universitas Indonesia, Kampus Depok, Jawa Barat 16424, Indonesia
Abstract
Abstract. HOTS is the important concept in Indonesian curriculum 2013 reform. Combinatoric is one of the mathematic-s branch that can give an experience to the students to increase their HOTS. One of research topic in combinatorics is the rainbow connection number of a graph. Let G=(V,E) be a nontrivial connected graph on which is defined a coloring c:E(G)→{1,2,3,… ,k},k ∈ N, where adjacent edges may be assigned the same color. A path u-v in G is a rainbow path if all edges in the path have different colors. In this case, the coloring c is called a k-rainbow coloring of G where k is the number of color used. The minimum k for which G being rainbow-connected is called the rainbow connection number rc(G) of G. If for every pair u,v ϵ G, G contains a rainbow u-v geodesic, then G is called strongly rainbow-connected. The minimum k for which G being strongly rainbow-connected is called the strong rainbow connection number src(G) of G. In this paper we determine the exact value of rc(G) and src(G) for grid-3D graph.
Keywords: HOTS, Rainbow connection number, Strong rainbow connection number, Grid 3D graph
Topic: Mathematics Education