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GATE | GATE-IT-2004 | Question 37

  • Difficulty Level : Medium
  • Last Updated : 10 Sep, 2018

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 


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