Consider a connected graph with n vertices; if n - 1 of the vertices have degree 1, then the graph is a tree.
A) This statement is always true.
B) This statement is always false.
C) This statement is always true if and only if one vertex has degree n - 1.
D) This statement is only false if and only if one vertex has degree n - 1.
E) None of the above.

Question

Quizplus · Accepted Answer

In a connected graph with n vertices where n - 1 vertices have degree 1, the remaining vertex must connect to all other vertices to maintain connectivity, giving it a degree of n - 1. This forms a star graph, which is a special case of a tree.

Consider a Connected Graph with N Vertices; If N -