Question

Using the handshaking principle,determine the number edges of a graph with fourteen vertices and each with degree six

Answer 1

Find the sum of all degrees of vertices in the graph:

$\sum deg\;v = 6*14=84$

By handshaking lemma,

$\sum deg\;v = 2 \cdot |E|$

Then the number of edges in the graph is

$|E| = \frac{{84}}{2} = 42$

Answer: 42