GATE CS 2014 Set 3 — Question 61
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Engineering Mathematics → Graph Theory (Math) → Connectivity
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Question
If is a forest with vertices and connected components, how many edges does have?
Correct answer
(C) n - k
Solution
A forest is a collection of disjoint trees. Let the forest have connected components (trees) denoted by .
Let be the number of vertices in the -th component . Then, the total number of vertices is .For any tree with vertices, the number of edges is .
Therefore, the number of edges in is .The total number of edges in the forest is the sum of the edges in each component:Thus, the number of edges is .
Let be the number of vertices in the -th component . Then, the total number of vertices is .For any tree with vertices, the number of edges is .
Therefore, the number of edges in is .The total number of edges in the forest is the sum of the edges in each component:Thus, the number of edges is .
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