On The Rainbow Connection Of Middle Graph Of Firecracker Graphs (F_(n,4)) - Rahim, Delvira Masita; Nurwan, Nurwan; Yahya, Nisky Imansyah; Wungguli, Djihad; Arsal, Armayani (JMEA : Journal of Mathematics Education and Application, 2025)
Coloring in graph theory includes various approaches, one of which is rainbow coloring which is closely related to the concept of rainbow connected numbers which refers to the least number of colors needed to color the edges in a graph so that every two vertices connected in a rainbow path have the same color and is denoted by rc(G). Rainbow coloring can be studied in several forms of graph development, one of which is the middle graph. All types of graphs, both simple and complex, can be represented as a middle graph. A middle graph is a graph whose vertices are obtained from the vertices and edges of graph G and is denoted by V (M(G)) = V (G)∪(G). Two points in a middle graph are considered adjacent if and only if they are adjacent edges in G or one of the points is adjacent to an edge of G. In this research, we discuss the number rc(G) on the middle graph of firecracker graph (F_(n,4)) with n ≥ 2. Based on the research results, we obtain the rainbow connected number theorem on the middle graph of firecrackers graph rc(M(F_(n,4))) = 3n + 2 for n ≥ 2.