A connected undirected graph that has n vertices and exactly n - 1 edges cannot contain a cycle.

Question

Quizplus · Accepted Answer

This is true because for a graph to contain a cycle, it must have at least n edges (where n is the number of vertices) according to the definition of a cycle. Therefore, if a graph has exactly n - 1 edges, it cannot contain a cycle. Additionally, the fact that the graph is connected ensures that every vertex is reachable from every other vertex, so there is no possibility of an isolated disconnected cycle.

A Connected Undirected Graph That Has N Vertices and Exactly