UGC NET CSE | December 2005 | Part 2 | Question: 1

Question

$T$ is a graph with n vertices. $T$ is connected and has exactly $n-1$ edges, then :

• A. $T$ is a tree
• B. $T$ contains no cycles
• C. Every pairs of vertices in $T$ is connected by exactly one path
• D. All of these

Answer 1

Ans :D All of these

Remember:

• A tree with n vertices has n−1 edges.
• Any connected graph with n vertices and n−1 edges is a tree
• For a tree (T), there is one and only one path between every pair of vertices in a tree.
• A tree is a connected graph containing no cycles