Solution Found!
Suppose G is a disconnected graph with no circuits. Let N denote the number of vertices
Chapter 7, Problem 52(choose chapter or problem)
Suppose G is a disconnected graph with no circuits. Let N denote the number of vertices, M the number of edges, and K the number of components. Explain why M = N - K. (Hint: Try Exercise 51 first.)
Questions & Answers
QUESTION:
Suppose G is a disconnected graph with no circuits. Let N denote the number of vertices, M the number of edges, and K the number of components. Explain why M = N - K. (Hint: Try Exercise 51 first.)
ANSWER:Step 1 of 3
A disconnected graph () is one without any circuits and at least two components. The number of components is , the number of edges is , and the number of vertices is . Since there are no circuits in , each component must be a tree. In light of the fact that a component is a tree if it has edges and vertices.