Let G(V, E) be a connected, undirected and simple graph with vertex set V(G) and edge set E(G). A labeling of a graph G is a bijection f from V(G) to the set {1, 2,…, | V(G)|}. The bijection f is called rainbow antimagic vertex labeling if for any two edge uv and u’v’ in path x — y,w(uv) = w(u’v’) w(uv), where w(uv) = f (u) + f (v) and x,y ∈ V(G). A graph G is a rainbow antimagic connection if G has a rainbow antimagic labeling. Thus any rainbow antimagic labeling induces a rainbow coloring of G where the edge uv is assigned with the color w(uv). The rainbow antimagic connection number of G, denoted by rac(G), is the smallest number of colors taken over all rainbow colorings induced by rainbow antimagic labeling of G. In this paper, we show the exact value of the rainbow antimagic connection number of jahangir graph J2,m, lemon graph Lem, firecracker graph (Fm,3), complete bipartite graph (K2,m), and double star graph (Sm,m).

Let G(V, E) be a connected and simple graphs with vertex set V and edge set E. Define a coloring c : E(G) → {1, 2, 3, …, k}, k ∈ N as the edges of G, where adjacent edges may be colored the same. If there are no two edges of path P are colored the same then a path P is a rainbow path. The graph G is rainbow connected if every two vertices in G has a rainbow path. A graph G is called antimagic if the vertex sum (i.e., sum of the labels assigned to edges incident to a vertex) has a different color. Since the vertex sum induce a coloring of their edges and there always exists a rainbow path between every pair of two vertices, we have a rainbow antimagic coloring. The rainbow antimagic connection number, denoted by rcA (G) is the smallest number of colors that are needed in order to make G rainbow connected under the assignment of vertex sum for every edge. We have found the exact value of the rainbow antimagic connection number of ladder graph, triangular ladder, and diamond.

Students' metacognition skills are expected to improve with the implementation of STEM-based learning. This research aims to analyze the implementation of STEM-based learning and its effect on students' metacognition skills in solving social arithmetic problems. The method used in this study is a mixed method, which combines qualitative and quantitative methods. The research subjects were elementary school students consisting of 11 experimental class students and 11 control class students. Both classes were given different treatments. The instruments of this study were tests, observations, and interviews. Quantitative methods are used to analyze differences in student learning outcomes in both classes, while qualitative methods are applied to analyze students' metacognition skills. The results showed that there were significant differences between the two classes applying STEM-based learning and conventional learning models. Statistical results show that the significance of the 2-tailed t-test independent sample in the post-test is 0,000 or α ≤ 0.05. It shows that the implementation of STEM-based learning significantly influences students' metacognition skills in solving social arithmetic problems. Based on the results of the phase portrait analysis, it is known that students in the control class have relatively low metacognition skills and the experimental class has relatively higher metacognition skills which can be seen from the number of indicators mastered by each student.

The study aims to investigate students’ creative-innovative thinking skill in solving rainbow antimagic coloring on research based learning model. The method used in this study is a mixed method, i.e. combining the qualitative and quantitative methods. The research subjects were 4th semester of students of higher education consisting of 41 students of experimental class and 30 students of control class. The instruments of this research are test, an observation, and an interview. Qualitative method is applied to analyze observation and development research, while quantitative method is applied to analysis the difference in student achievment result among two classes. The result show that there are significant difference between the two classes that applied research based learning and conventional learning models. The statistical result indicates that the (2-tailed) significance of the independent sample t-test in the post-test was 0.000 or p < 0.05. It implies that the implementation of RBL, significantly influenced the students’ creative-innovative thinking skill in solving rainbow antimagic coloring.