#star graph

(Star Graph)

Line Graphs I An edge graph of a graph G, represented L(G), is where you take all the edges (connections between vertices) of G, and use that as the set vertices in L(G), and if two edges touch the same vertex in G, then they are connected in L(G). The star graph, where one point is connected to every other point, and those other points are not connected to each other, can be thought of as the complete bipartite graph, K1,n-1, meaning that it can be split into two groups, one with 1 element, and the other with n-1 elements, where each member of one group is connected to every member of the other, but none in the same group. It has n-1 edges, so its line graph has n-1 vertices, and all of them are connected to every other one, because they all share the center vertex. This means that it is the complete graph Kn-1.