Find all loopfree undirected graphs with four vertices up to

Find all loop-free undirected graphs with four vertices up to a graph isomorphism. How many of these have no pendant vertices?

6. Find all loop-free undirected graphs with four vertices up to a graph isomor- phism. How many of these have no pendant vertices?

Solution

Let the two graphs be G and H. An isomorphism of G and H is a bijection between the vertex sets of G and H.

Loop free undirected graph is called simple graph.In undirected graph the degree of a vertex is equal to the number of adjacent vertices.Therefore , there is only one undirected graph for four vertices, in which all four vertices are connected to each other as in the shape of square.

Pendent vertex is a certex of a graph if its neighborhood contains exactly one vertex.So, the discribed four vertices graph heve no any pendent vertex.