Determining the Number of Disconnected Vertices Labeled Graphs of Order Six with the Maximum Number Twenty Parallel Edges and Containing No Loops

Abstract

If there exist two vertices on a given graph that are not connected by a path, then we call that graph is disconnected. Given a graph with n vertices and m edges, then a lot of graphs can be constructed. In this paper, we discuss the number of disconnected vertices labeled graphs of order six (n = 6) with the maximum number of parallel edges is twenty. Moreover, a maximum number of edges that connect different pair of vertices is ten (parallel edges are counted as one) and containing no loops (isomorphic graphs are counted as one).