Question: Let G be a simple graph with 15 vertices and 4 connected components. Prove that G has at least one component with at least 4

Let G be a simple graph with 15 vertices and 4 connected components. Prove that G has at least one component with at least 4 vertices. What is the largest number of vertices that a component of G have? Compute the maximum number of edges of G?

Step by Step Solution

★★★★★

3.45 Rating (161 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Suppose that if all the four components have at most ... View full answer

Question Has Been Solved by an Expert!

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

Step: 2 Unlock

Step: 3 Unlock

Document Format (2 attachments)

60a23d5f4c3d9_213177.pdf

180 KBs PDF File

60a23d5f4c3d9_213177.docx

120 KBs Word File

Students Have Also Explored These Related Computer Engineering Questions!

Let G be a simple graph with n vertices. Show that a) G is a tree if and only if it is connected and has n - 1 edges. b) G is a tree if and only if G has no simple circuits and has n 1 edges.

What is the largest number of linearly independent matrices one can have in M(3, 2)? Prove your answer

What is the largest number of electrons with the same pair of values for n and that an atom can have? (tutorial: neon atom)

In multiple regression analysis, explain why the typical hypothesis that analysts want to test is whether a particular regression coefficient (B) is equal to zero (H0: B = 0 ) versus whether that...

Suppose that the demand curve for a product x provided by a monopolist is given by p = 90x and suppose further that the monopolists marginal cost curve is given by MC = x. A: In this part, we will...

Show that if G is a simple graph with n vertices, then the union of G and is Kn.

Find a self-complementary simple graph with five vertices.

Give a big-O estimate of the number of operations (comparisons and additions) used by Floyd's algorithm to determine the shortest distance between every pair of vertices in a weighted simple graph...

(a) Let G be an undirected graph with n vertices. If G is isomorphic to its own complement , how many edges must G have? (Such a graph is called self-complementary.) (b) Find an example of a...

Let G be a directed graph with N vertices. A vertex s is called a sink if, for every v in V such that s v, there is an edge (v, s), and there are no edges of the form (s, v). Give an O(N) algorithm...

Q4 Complete the following reactions schemes by drawing the messing intermediate/products: Me,CO - ZnCl, OH OMe "OH Ozonolysis OH

Determine whether the alternating series \ ( \ sum _ { n = 2 } ^ { \ infty } ( - 1 ) ^ { n + 1 } \ frac { 3 } { 5 \ ln n } \ ) converges or diverges. Choose the correct answer below and, if...

A depositor puts $25,000 in a savings account that pays 5% interest, compounded semiannually. Equal annual withdrawals are to be made from the account, beginning one year from now and continuing...

The contents of the stirred-tank heating system shown In figure are heated at a constant rate of Q(Btu/h) using a gas-fired heater. The flow rate w(lb/h) and volume V(ft3) are constant, but the heat...

In a particular situation, four mutually exclusive alternatives are being considered. Each of the alternatives costs $1300 and has no end-of-useful-life salvage value . If the MARR is 8%, which...

Three mutually exclusive projects are being considered: When each project reaches the end of its useful life, it would be sold for its salvage value and there would be no replacement. If 8% is the...

The market and Stock J have the following probability distributions: a. Calculate the expected rates of return for the market and Stock J. b. Calculate the standard deviations for the market and...

Which of the following statements about simple machines is true? Simple machines require electric energy to operate. Simple machines have many moving components. Simple machines cannot be used to...

5. (Thickness) Let G be a simple undirected graph with n vertices labeled 1,2,.. .n The graph Glr, r2,...,rn] is the graph obtained from G by replacing vertex i with K, and connecting all possible...

2.(20 pts) Let G be a simple graph (no loops or multi-edges) and G1 denote the complement of G. It is known that the number of edges in G and G1 are 15 and 30, respectively. It is further known that...

Im currently confused and need help with this homework . I have no idea where to start ; if anyone can help me with these 6 problems and explain it to me. I would really appreciate it. This is Graph...

la) What is the face chromatic number of the graph at the right? b) What is the edge chromatic number of the graph at the right? 2. Find the chromatic polynomial for the graph on the right. P A B L b...

Let G be a simple, directed graph with positive edge weights. Let G' the same graph except where each edge is increased by a constant value c > 0. Let P be the shortest path from vertex s to vertex t...

a ) Let G be a simple undirected graph. If it has n vertices, what is the maximum number of edges it could have? b ) Let G be a simple undirected graph with n = 4 vertices and 6 edges having weights...