Questions: Which of the following graphs are trees?

{ "options": [ { "isCorrect": "yes", "label": "1", "text": "A graph with 5 vertices and 4 edges, where all vertices are connected." }, { "isCorrect": "no", "label": "2", "text": "A graph with 5 vertices and 5 edges, where all vertices are connected." }, { "isCorrect": "yes", "label": "3", "text": "A graph with 5 vertices and 4 edges that is disconnected." }, { "isCorrect": "no", "label": "4", "text": "A graph with 5 vertices, 5 edges, and no cycles." } ], "explanation": "A tree is a connected graph with no cycles. Equivalently, a tree with n vertices has n-1 edges. \n\nOption 1: A connected graph with 5 vertices and 4 edges is a tree.\nOption 2: A connected graph with 5 vertices and 5 edges must contain a cycle, so it is not a tree.\nOption 3: A disconnected graph is not a tree, regardless of the number of vertices and edges.\nOption 4: A graph with 5 vertices, 5 edges, and no cycles cannot exist. If it has no cycles, it must be disconnected to have 5 edges." }