The study of metric dimension of graph G has widely given some results and contribution of graph research of interest, including the domination set theory. The dominating set theory has been quickly growing and there are a lot of natural extension of this study, such as vertex domination, edge domination, total domination, power domination as well as the strong domination. In this study, we initiate to combine the two above concepts, namely metric dimension and strong domination set. Thus we have a resolving strong domination set. We have obtained the resolving strong domination number, denoted by γrst(G), of some graphs.

Let G be a simple connected graph, an ordered pair of sets G(V, E), with V is a set of vertices and E is a set of edges. Graph coloring has been one of the most popular branches in topics of graph theory. In 2017 Arumugam et al. developed a new notion of coloring, namely local antimagic coloring of a graph. This concept is a combination of graph labeling and graph coloring. The local antimagic of graphs is one of the colorings of graph theory that is interesting to study. By the definition, the local antimagic coloring is a bijection f : E(G) ƒ> {1, 2, 3,…, |E(G)|} if for any two adjacent vertices u and v, w(u) = w(v), where w(v) = ΣeeE(v) f (e), and E(u) is the set of edges incident to u. Thus any local antimagic labeling induces a proper vertex coloring of G where the vertex v is assigned the color w(v). The local antimagic chromatic number xla(G) is the minimum number of colors taken over all colorings induced by local antimagic labelings of G. In this paper, we will study the local antimagic coloring of amalgamation of graphs.

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Problem-solving can grow if students are trained to have metaliteracy. Metaliteracy is the ability to think that focuses on critical thinking skills and collaborative efforts. This study aims to determine the impact of the implementation of RBL-STEM to analyze the metaliteracy of students in solving rainbow antimagic coloring problems. The methods used in this study were a combination of quantitative and qualitative methods. This research used two classes, experimental and control. Both classes were given the same treatments with different experiment classes using LKM that have been developed with the RBL model. The analysis of the results of the homogeneity test on the pre-test items showed that the two classes were homogeneous with a significant value is ≥ 0.05, and the results of the independent sample t-test on post test result showed that the sig (2-tailed) value is 0.000 (p ≤ 0.05) so its significant. It can be concluded that the RBL-STEM model can improve the metaliteracy level of the students in solving rainbow antimagic coloring.