Exercise · ZW-TREE-010 · ★★★ Advanced
Which of the following statements is true for every tree?
Choose one option.
Show answer
- B. Between each pair of vertices there is exactly one simple path
Explanation
At least one path exists because it is connected, and two different paths would form a cycle. The others fail: a path on 3 vertices has leaves, a tree has one edge fewer than vertices, and in a long path no vertex is adjacent to all others.
Review the concept: Tree
A tree \(T=(V,E)\) is a connected graph that contains no cycles.
\[|E|=|V|-1\]
More practice problems: tree
- ZW-TREE-001 How many edges does a tree with 10 vertices have?
- ZW-TREE-002 A tree has 15 edges. How many vertices does it have?
- ZW-TREE-003 The vertices are 1,dots,5. Which of these edge sets forms a tree?
- ZW-TREE-004 What is the sum of the vertex degrees of a tree with 7 vertices?
- ZW-TREE-005 A tree with 7 vertices has one vertex of degree 4, one of degree 3, and the rest are leaves (degree…
- ZW-TREE-006 One edge is removed from a tree. How many connected components does the resulting graph have?
- ZW-TREE-007 How many different trees are there on labeled vertices 1,2,3,4?
- ZW-TREE-008 An acyclic graph has 10 vertices and 3 connected components. How many edges must be added, without…