For a given graph G having v vertices and e edges which is connected and has no cycles, which of the following statements is true?

Category: QuestionsFor a given graph G having v vertices and e edges which is connected and has no cycles, which of the following statements is true?
Editor">Editor Staff asked 4 weeks ago

For a given graph G having v vertices and e edges which is connected and has no cycles, which of the following statements is true?
 
(a) v=e
 
(b) v = e+1
 
(c) v + 1 = e
 
(d) v = e-1
 
My doubt is from Graph topic in portion Graph of Data Structures & Algorithms I
 
I had been asked this question in an international level competition.

1 Answers
Editor">Editor Staff answered 4 weeks ago

Correct answer is (b) v = e+1
 
For explanation: For any connected graph with no cycles the equation holds true.