Bilangan Terhubung Titik Pelangi Pada Amalgamasi Graf Berlian

Abstract

Suppose there is a simple, and finite graph G = (V, E). The coloring of vertices c is denoted by c: E(G) → {1,2, ..., k} with k is the number of rainbow colors on graph G. A graph is said to be rainbow connected if every pair of points x and y has a rainbow path. A path is said to be a rainbow if there are not two edges that have the same color in one path. The rainbow connected number of graph G denoted by rc(G) is the smallest positive integer-k which makes graph G has rainbow coloring. Furthermore, a graph is said to be connected to rainbow vertex if at each pair of vertices x and y there are not two vertices that have the same color in one path. The rainbow vertex connected to the number of graph G is denoted by rvc(G) is the smallest positive integer-k which makes graph G has rainbow coloring. This paper discusses rainbow vertex-connected numbers in the amalgamation of a diamond graph. A diamond graph with 2n points is denoted by an amalgamation of a diamond graph by adding the multiplication of the graph t at point v is denoted by Amal (Brn,v,t).

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

“…Several studies have been carried out, namely examining rainbow-connection numbers on the results of amalgamation operations of several special graphs, such as what was done by Fitriani and Salman in 2016 [6]. Then, in 2019, several studies were carried out on the amalgamation of diamond graphs, including those carried out by Afifah et al [7] and Cindy et al [8]. Therefore, from several studies that have been done previously, the author tried to develop rainbow connection numbers by adding amalgamation operations from two special graphs.…”