Find the number of vertices the number of edges and the degr

Find the number of vertices, the number of edges and the degree of each vertex in the undirected graph. Identify all isolated and pendant vertices. Find the sum of the degrees of the vertices and verify the Handshaking Theorem. State explicitly what this is equal to in terms of the edges.

Solution

We can see that there are 5 vertices, namely, a, b, c, d and e. Therefore,

Number of vertices = 5

Number of edges: 13

Degree of each vertex:

Vertex a : Degree is 6

Vertex b: Degree is 6

Vertex c: Degree is 6

Vertex d: Degree is 5

Vertex e: Degree is 3

There are no isolated vertices as the given graph is connected.

There are no pedant vertices as there are no leafs (vertices with degree 1)

Sum of degrees of vertices = (6+6+6+5+3) = 26

Number of edges = 13

Therefore, Sum of degrees of vertices = 2*(Number of edges)

Hence, the handshake theorem is verified!