The Formula to Count The Number of Vertices Labeled Order Six Connected Graphs with Maximum Thirty Edges without Loops

Abstract If for every pair of vertices in a graph G(V,E) there exist minimum one path joining them, then G is called connected, otherwise the graph is called disconnected. If n vertices and m edges are given then numerous graphs are able to be created. The graphs created might be disconnected or connected, and also maybe simple or not. A simple graph is a graph whose no paralled edges nor loops. A loop is an edges that connects the same vertex while paralled edges are edges that connecting the same pair of vertices. In this research we will discuss the formula to count the number of connected vertex labeled order six graph containing at most thirty edges and may contain fifteen parallel edges without loops.