A tree is :
A. a circuitless connected graph
B. a connected graph of 'n' vertices with (n − 1) edges
C. a circuitless graph of 'n' vertices with (n − 1) edges
D. a minimally connected graph
Choose the correct answer from the options given below :

Explanation

All four statements are standard, mutually equivalent characterizations of a tree on n vertices. Statement A is the basic definition (connected and acyclic). Statement B holds because a connected graph on n vertices with exactly n−1 edges must be acyclic, hence a tree. Statement C holds because an acyclic graph on n vertices with n−1 edges must be connected, hence a tree. Statement D holds because removing any single edge from a tree disconnects it, so a tree is precisely a minimally connected graph, making A, B, C and D all correct.