The Rainbow Connection Number of Snail Graphs

Abstract

Several previous studies have investigated the rainbow connection number. This research aims to determine the rainbow connection number of the snail graph. The snail graph, denoted by Sln , is constructed from a triangular book subgraph BTn whose common spine is amalgamated with the cycle C4, then two pendant vertices are added and attached to one of the end-vertices of the amalgamated spine. The rainbow connection number of a connected graph G, written rc(G), is defined as the minimum number of colors required so that G becomes rainbow connected. This study is a qualitative descriptive research. The method used is literature study, and the data analysis technique is non-statistical data analysis. From the results, it is found that the rainbow connection number of the snail graph is:4 when n=1;4 when n=2;5 when n=3;5 when n=4; and6 for all n≥5.