Show that in a simple graph with at least Two vertices there must be two vertices that have the same degree.

Two simple graphs are if there is a bijection from the vertices of the first graph to the vertices of the second such that two vertices are adjacent in the first graph if and only if their images are adjacent in the second.

Draw a graph with four vertices in which two vertices are of degree 2 and two vertices are of degree 3

determine the number of vertices and edgesand find the in-degree and out-degree of each vertex for the given directed multigraph.

What is the vertex