My first instinct was to say true and move on because that's the tree property everyone knows.
State that the statement is true, then provide a proof using induction or the fact that a forest with N nodes and C components has N-C edges. Also, connect it to the concept of a tree having exactly N-1 edges.
Pro tip: Mention that this property is fundamental in graph theory and is used in algorithms like Kruskal's for cycle detection. Showing awareness of practical applications demonstrates deeper understanding.
Define acyclic undirected graph (forest) and note that a tree is a connected acyclic graph.
Clearly state that the statement is true: an acyclic undirected graph with N nodes has at most N-1 edges.
Use induction: start with N=1 (0 edges), add a node and at most one edge to maintain acyclicity, or use the formula for a forest: edges = N - components ≤ N-1.
Explain that equality holds if and only if the graph is connected (i.e., a tree).
Briefly note that this property is used in cycle detection and minimum spanning tree algorithms.
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