GATE CS 2017 Set 1 — Question 20
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Engineering Mathematics → Graph Theory (Math) → Graph Terminology (Degree, Paths, Cycles)
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Question
Let be a tree with 10 vertices. The sum of the degrees of all the vertices in is ________ .
Correct answer
18 to 18
Solution
For any tree with vertices, the number of edges is .
Given , the number of edges is .According to the Handshaking Lemma, the sum of degrees of all vertices in a graph is equal to twice the number of edges:
Given , the number of edges is .According to the Handshaking Lemma, the sum of degrees of all vertices in a graph is equal to twice the number of edges:
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