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In discrete mathematics and computer science, atreeis a special kind ofgraph. The standard graph-theory definition is that a tree is aconnected, acyclicundirected graph. “Acyclic” means it containsno cycles, i.e., you cannot start at a vertex, follow a sequence of edges, and return to the starting vertex without repeating edges in a way that forms a loop. (Wikipedia) This property is exactly what makes option D correct.

The other options contradict the definition. If a structure has cycles, it is not a tree (though it may still be a graph). If it has unconnected nodes, it is not connected; such a structure is more like aforest(a disjoint union of trees) rather than a single tree. (Wikipedia) The idea of “levels” belongs to a particular computer-science representation called arooted tree, where one node is chosen as the root and nodes can be assigned depths/levels based on distance from the root. But levels are not required in the abstract definition of a tree as a graph; they arise from choosing a root and orientation for convenience in algorithms like BFS/DFS, heaps, and parse trees.

So, the relationship is: every tree is a graph with extra structure—specifically, no cycles and (typically) connectivity—and the “no cycles” rule is the key distinguishing feature. (Discrete Mathematics)