GATE | GATE-IT-2004 | Question 37
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?
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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