Question: Prove: Let G be a graph with n vertices and q edges and let k(G) denote the number of connected components of G. Then G

Prove:

Let G be a graph with n vertices and q edges and let k(G) denote the number of connected components of G. Then G has at least n-k(G) edges, i.e., q >= n-k(G).

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Databases Questions!

The quantitative methods department head at a major midwestern university will be scheduling faculty to teach courses during the coming autumn term. Four core courses need to be covered. The four...

1. Finding a small coloring Let G be a graph of n vertices with chromatic number (G). Suppose that you cannot directly access G. Fortunately, you can access G via an oracle that behaves as follows....

According to the following graph just answer this two questions : 1-Let G be a graph with n vertices and m edges. a. True or false: All its DFS forests (for traversals starting at different vertices)...

a) Give a counterexample to the claim in the Theorem. b) Identify the mistake in the "proof."

USING PYTHON!!!! USING PYTHON!!!! USING PYTHON!!!! USING PYTHON!!!! USING PYTHON!!!! Problem 2: Diameters of random graphs Grading criteria: code correctness for a; soundness of methodology and...

[Python and Sage Question] All computations should use the SageMath 9.0 kernel. However, you are free to mix Python and Sage functionality in your code. Problem 2: Diameters of random graphs Grading...

Marks: /18 DGD (circle one): DGD1 (in DMS1120 ) DGD2 (in STEB0138 ) MAT 1348B (Prof. P. Scott) Tenth Homework Assignment (Updated) Due Friday, April 10 by 9:00 AM. Instructions: Print out this...

A knight in chess is a piece that can move either two squares horizontally and one square vertically, or one square horizontally and two squares vertically. A knight's tour is a sequence of legal...

Question 4: Counting Problems of the questions below, your answer must consist of a formula in vertices n, along with a brief but concise justification of its correctness. Answers without sufficient...

Problem 4: A Graphic Flaw 15 Find a counterexample to the following false claim, and identify the error in the proof Claim 11. For every undirected graph G- (V, E) without loops, if Vl 2 3 and every...

Sabert manufactures the Mosac line of heavyweight plastic cutlery. Colored a distinctive silver, Mosacs products allow one to entertain with more style. Currently, Sabert offers two combo...

If the price of eggs were to double from $1 per egg to $2 per egg, Freddy would consume 6 fewer eggs without changing his consumption of other goods. Which would he prefer: The price increase, or...

An all - equity firm is evaluating a capital project that has the same level of risk as the firm. The project should be accepted if it s:

Seved Help 14 Wisconsin Snowmobile Corp. is considering a switch to level production Cost efficiencies would occur under level production, and aftertax costs would decline by $31,500, but inventory...

What are Decision Trees?

What is meant by the Term Glass Ceiling?

What Interface is used to develop Data Mining Structures in SQL Server Analytical Databases?