What is the number of vertices in an undirected connected graph with 27 edges, 6 vertices of degree 2, 3 vertices of degree 4 and remaining of degree 3?
(A) 10
(B) 11
(C) 18
(D) 19
Answer: (D)
Explanation: The idea is to use Handshaking Lemma :- In any graph, the sum of all the vertex-degree is equal to twice the number of edges.
Let x = Total Number of Vertices. By Handshaking Lemma 6*2 + 3*4 + (x-9)*3 = 27*2 24 + (x-9)*3 = 54 x-9 = 10 x = 19