ISRO CS 2009

Question 1

If G is a graph with e edges and n vertices, the sum of the degrees of all vertices in G is

Question 1 Explanation:

Handshaking theorem states that the sum of degrees of the vertices of a graph is twice the number of edges.

If G=(V,E) be a graph with E edges,then-

Σ deg_G(V) = 2E

This theorem applies even if multiple edges and loops are present.

Since the given graph is undirected, every edge contributes as twice in sum of degrees. So the sum of degrees is 2e.

Correct Answer: D

Question 1 Explanation:

Handshaking theorem states that the sum of degrees of the vertices of a graph is twice the number of edges.

If G=(V,E) be a graph with E edges,then-

Σ deg_G(V) = 2E

This theorem applies even if multiple edges and loops are present.

Since the given graph is undirected, every edge contributes as twice in sum of degrees. So the sum of degrees is 2e.