True or false: If an undirected graph 𝐺G on 𝑛n vertices is connected and has at most 𝑛−1n−1 edges then 𝐺G must be a tree.TrueFalseSubmit
Question
True or false: If an undirected graph 𝐺G on 𝑛n vertices is connected and has at most 𝑛−1n−1 edges then 𝐺G must be a tree.TrueFalseSubmit
Solution
True.
An undirected graph G on n vertices is a tree if it is connected and has exactly n-1 edges. If it has at most n-1 edges and is still connected, it must be a tree. This is because adding any more edges would create a cycle, which would violate the definition of a tree.
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