Which of the following graphs are trees ? Choose the correct answer from the…

Key idea: A graph is a tree if and only if it is connected and contains no cycles. For a graph with n vertices, a tree has exactly n−1 edges.

• First (topmost) diagram: vertices a, b, c, d, e, f. Edges are c–a, c–b, c–d, c–f and f–e (5 edges). The graph is connected and has no cycles, so it is a tree.

• Second diagram: vertices a, b, c, d, e, f. Edges include a–c, a–f, b–e, e–f and f–d (5 edges). This graph is connected and contains no cycles, so it is a tree.

• Third diagram: this diagram has multiple crossing edges that create closed loops (cycles). Because it contains cycles, it is not a tree.

• Fourth (bottommost) diagram: the vertices split into at least two components (one component containing a and f, another containing b, d, e, c), so the graph is disconnected and therefore not a tree.

Conclusion: Only the first and second diagrams are trees, so the correct choice selects those two diagrams.