Suppose G is r regular with n vertices and m edges Show that

Suppose G is r -regular, with n vertices and m edges. Show that either r is even or n is even.

Solution

Solution:  A graph in which every vertex has the same degree is called a regular graph. If all vertices have degree r, the graph is said to be r-regular. For any vertex v in a graph, the degree of the vertex is equal to the number of edges which contain the vertex.

So if G has n vertices and the number is two then they have one edge which contains the vertices and it is odd and when number of vertices are three then number of edges is two which is even. So either r is even or n is even.