please no hand writing please no hand writing State the Hand

please no hand writing please no hand writing

State the Handshaking theorem and verify it for the following undirected graph

Solution

Answer :

THEOREM OF THE DAY

The Handshaking Lemma :

In any graph the sum of the vertex degrees is equal to twice the number of edges.

In the given graph ,

degree(a) = 2

degree(b) = 3

degree(c) = 2

degree(d) = 3

degree(e) = 2

degree(f) = 3

degree(g) = 2

degree(h) = 3

So the sum of the degrees of the vertices is 2 + 3 + 2 + 3 + 2 + 3 + 2 + 3 = 20

And the number of edges = 10.

Clearly , sum of the degrees of the vertices(20) = 2(number of edges(10) )

Hence, Handshaking Lemma is verified.