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Determine the number of edges in a graph with 6 nodes, 2 nodes of degree 4 and 4 nodes of degree 2. Draw two such graphs.
1 Answer
written 8.2 years ago by | • modified 8.2 years ago |
Suppose the graph with 6 vertices has e number of edges. Therefore by Handshaking Lemma
6∑i=1deg(vi)=2e
⇒d(v1)+d(v2)+d(v3)+d(v4)+d(v5)+d(v6)=2e
Now, given 2 vertices are of degree 4 and 4 vertices are of degree2.Hence the above equation,
(4+4)+(2+2+2+2)=2e⇒16=2e⇒e=8
$\text{Hence the number of efges in …