Exercise · ZW-TREE-009 · ★★★ Advanced
An edge is added to a tree between two vertices that were not adjacent. The result:
Choose one option.
Show answer
- A. Is connected and has exactly one cycle
Explanation
It stays connected (an edge was only added). There was a single path between those vertices; together with the new edge it closes exactly one cycle.
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…