Question: (a) Explain why it is not possible to draw a loop-free connected undirected graph with eight vertices, where the degrees of the vertices are 1,

(a) Explain why it is not possible to draw a loop-free connected undirected graph with eight vertices, where the degrees of the vertices are 1, 1, 1, 2, 3, 4, 5, and 7.
(b) Give an example of a loop-free connected undirected multigraph with eight vertices, where the degrees of the vertices are 1, 1, 1, 2, 3, 4, 5, and 7.

Step by Step Solution

★★★★★

3.55 Rating (169 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a Let a b c x y V with dega degb degc 1 degx 5 and degy 7 Since deg... 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 (1 attachment)

954-M-L-A-L-S (8134).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

A novel alternative medical treatment for heart attacks seeds the damaged heart muscle with cells from the patients thigh muscle (Doctors Mend Damaged Hearts with Cells from Muscles, San Luis Obispo...

Table 4.6 is a table with two rows and three columns, similar to the interaction effect term in the two-way factorial diagram in Figure 4.4. However, for this question we will assume that only two...

A study by Heffner, Drawbaugh, and Zigmond (1974) investigated the effects of an amphetamine on the behavior of rats. Before the study began, 24 "thirsty" rats were trained to press a lever to obtain...

Please help with answering this question. And show how so i can understand 19. a) Explain why it is not possible to draw a loop-free con- nected undirected graph with eight vertices, where the de-...

a ) Explain why it is not possible to draw a loop - free con - nected undirected graph with eight vertices, where the de - grees of the vertices are 1 , 1 , 1 , 2 , 3 , 4 , 5 , and 7 .

Connected Components. ( a ) ( 5 points ) Is it possible to draw an undirected, unweighted, simple graph with exactly 7 vertices, 1 1 edges, and 3 connected components? If so , then give the graph. If...

Draw a graph with eight vertices that is connected Where each vertex has: (a) (1 point) degree 2 (h) (1 point] degree 3 (c) (1 point] degree 4 (d) (2 points) Do all graphs with 8 vertices having...

Question 1 (1 point) When repesenting a graph as an adjacency list, space is saved compared to representation as an adjacency matrix. 1) True 2) False Save Question 2 (1 point) The following are the...

2. Assume that G is an undirected graph with 10 vertices and the following set of edges {a.bj, {a,d;, {a.h), (a.j), {b.c), {b,e), {cj), {c,ft, {c,h), {d.gj, {e,g), {e,h;, {e.ij, {ijj Give a valid...

break these questions down and explain why the answers are these 1. (4pts) (A) What is the MAXIMUM mad MINIMM oumber of EDGEs that a connected graph with 16 (sixteen) ventices cau liave? (6pts) (B) A...

QUESTION Nova Hair Solutions Berhad is factory that manufactures special head to toe body shampoo that is suitable for both kids and adults. Given are the updated standard costs used as benchmark for...

Water flows in a pipe at 0.015 m3/s. The pipe is 50 mm bore diameter. The pressure drop is 13 420 Pa per metre length. The density is 1000 kg/m3 and the dynamic viscosity is 0.001 N s/m. Determine i....

\ ( \ $ 7 3 , 7 0 0 \ ) . a . Find the operating break - even point in number of books. b . Calculate the total operating costs at the break - even volume found in part ( a ) . c . If Barry estimates...

Gable, the owner of a lumber company, was cutting trees over the boundary line between his property and prop erty owned by Lane. Although he realized he had crossed onto Lanes property, Gable...

A pendulum consists of a mass, called a bob, that is affixed to the end of a string of length L (see Figure 6.24). When the bob is moved from its rest position and released, it swings back and forth....

Show that the solution set S of the second-order differential equation y" + ay' + by = 0 is a subspace of P.

Show that eP1 cos qt and eP1 sin qt are linearly Independent

Kentucky Hardware Company (KHC) is considering an investment project that requires a new machine for producing special tools. This new machine costs $1,000,000 and will be depreciated over 10 years...

The characteristic polynomial of a 5 5 matrix is given below. Find the eigenvalues and their multiplicities. Question 5 {1 point] The characteristic polynomial of a 5 x 5 matrix is giyen below. Find...

Find the mean hours of exercise per week by the participants. Find the variance of the hours of exercise per week by the participants. Determine if there is a linear relationship between the hours of...