Graph vs Tree Key Structural Difference in DSA Typescript - Key Differences

Recall & Review

beginner

What is the main structural difference between a graph and a tree?

A tree is a special type of graph that is connected and has no cycles, while a graph can have cycles and may not be connected.

beginner

Can a tree have cycles? Why or why not?

No, a tree cannot have cycles because it must be acyclic to maintain a hierarchical structure with a single path between any two nodes.

beginner

Is it possible for a graph to be disconnected? Explain.

Yes, a graph can be disconnected, meaning it can have multiple separate parts with no paths between some nodes.

beginner

What does it mean for a tree to be connected?

A tree is connected if there is exactly one path between any two nodes, meaning all nodes are reachable from the root.

intermediate

How does the number of edges in a tree compare to the number of nodes?

A tree with n nodes always has exactly n-1 edges, ensuring no cycles and full connectivity.

Which of the following is true about trees?

A They always have more edges than nodes.

B They have cycles.

C They can be disconnected.

D They are always connected and acyclic.

Trees are connected and have no cycles, which means they are acyclic.

Can a graph have multiple paths between two nodes?

A Only trees can have multiple paths.

B No, graphs always have a single path.

C Yes, graphs can have multiple paths.

D Only disconnected graphs can have multiple paths.

Graphs can have cycles and multiple paths between nodes.

How many edges does a tree with 7 nodes have?

A 6

B 7

C 8

D 5

A tree with n nodes has n-1 edges, so 7 nodes means 6 edges.

Which statement is false about graphs?

A Graphs must have exactly n-1 edges for n nodes.

B Graphs can be disconnected.

C Graphs can have cycles.

D Graphs can have multiple edges between nodes.

Only trees have exactly n-1 edges; graphs can have any number of edges.

What is a key property of a tree that distinguishes it from a general graph?

A It is always disconnected.

B It has exactly one path between any two nodes.

C It can have cycles.

D It can have multiple edges between the same nodes.

Trees have exactly one path between any two nodes, ensuring no cycles.

Explain the key structural differences between a graph and a tree.

Think about connectivity and cycles.

Describe why a tree cannot have cycles and how this affects its structure.

Consider what cycles would do to paths between nodes.