GATE CS 2017 Set 2 — Question 23
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Engineering Mathematics → Graph Theory (Math) → Graph Terminology (Degree, Paths, Cycles)
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Question
is an undirected graph with vertices and 25 edges such that each vertex of has degree at least 3. Then the maximum possible value of is ______.
Correct answer
16 to 16
Solution
According to the Handshaking Lemma, the sum of the degrees of all vertices in an undirected graph is equal to twice the number of edges:Given that the number of edges , we have:It is also given that each vertex has a degree of at least 3, i.e., for all . Summing this over all vertices gives:Substituting the value from the Handshaking Lemma:Since the number of vertices must be an integer, the maximum possible value of is 16.
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