FREE Trial

For n ¥ 1, let tn count the number of spanning trees for the fan on n + 1 vertices.

Question:

For n ‰¥ 1, let tn count the number of spanning trees for the fan on n + 1 vertices. The fan for n = 4 is shown in Fig. 12.53.
1 2 3 4

(a) Show that tn+1 = tn + ˆ‘nl=0 tl, where n ‰¥ 1 and t0 = 1.
(b) For n ‰¥ 2, show that tn+1 = 3tn - tn-1.
(c) Solve the recurrence relation in part (b) and show that for n ‰¥ 1, tn = F2n, the 2nth Fibonacci number.

Transcribed Image Text:

1 2 3 4

This problem has been solved!


Do you need an answer to a question different from the above? Ask your question!

Step by Step Answer:

Answer rating: 71% (14 reviews)

a Consider the case for n 4 shown in part a of the figure The five spanning s…View the full answer


answer-question
Answered By
tutor-profile-image
Shebla K
I am an MBA graduate having experience as an Assistant Professor at University level for two years. I always prepare well for a class as I believe that only if you become an ocean you can give a bucket of water. Being a teacher was not only my profession but also my passion.
5.00+ 1+ Reviews 10+ Question Solved
Related Book For  answer-question
Discrete and Combinatorial Mathematics An Applied Introduction

Discrete and Combinatorial Mathematics An Applied Introduction

ISBN: 978-0201726343

5th edition

Authors: Ralph P. Grimaldi

See More Books
View Solution
Create a free account to access the answer
Cannot find your solution?
Post a FREE question now and get an answer within minutes. * Average response time.
Question Posted: June 21, 2016 08:56:27
See More Questions

Students also viewed these Linear Algebra questions

Q:
Let G = (V, E) be the undirected connected "ladder graph" shown in Fig. 12.49. For n ¥ 0, let an count the number of spanning trees of G, whereas bn counts the number of these spanning trees that...
A:
a For the spanning trees of G there are two mutually exclusive and exhaustive cases i The edge x 1 y......
Q:
Let A, B be sets with |A| = m n = |B|, and let a(m, n) count the number of onto functions from A to B. Show that a(m, 1) = 1 when m n > 1. Il a(m, n) = nm
A:
Let B n 1 and A m Then f A B where f a b for all a A and b B is the on......
Q:
Consider the four comb graphs in parts (i), (ii), (iii), and (iv) of Fig. 11.96. These graphs have 1 tooth, 2 teeth, 3 teeth, and ft teeth, respectively. For n ¥ 1, let an count the number of...
A:
There are two cases to consider 1 The vertex y n is not used Then there are a n1 independent......
Q:
If two companies in the same industry use different methods to value inventory, this makes comparisons more difficult but not impossible. a. True b. False 2. An increase in a company's revenue and...
A:
1 True For example FIFO values can be obtained using LIFO......
Q:
NET how might the following organizations use an Internet chat room for exploratory research? a. A provider of health benefits b. A computer software manufacturer c. A video game manufacturer
A:
Each of these organizations could use the Internet for exploratory research a A provider of healt......
Q:
An acceptable use policy is an example of a(n) ________ control.
A:
An acceptable use policy is an example of a n administrative control An administrative control is a......
Q:
For each of the following lists of premises, derive the conclusion and supply the justification for it. There is only one possible answer for each problem.
A:
Click to View...
Q:
The balance sheet and income statement for the J. P. Robard Mfg. Company are as follows: J. P. Robard Mfg., Inc. Balance Sheet ($000) Cash ..........................$ 500 Accounts receivable...
A:
We are asked to find various ratios for the J P Robard Manufacturing Company Some of these ratios use only balance sheet data the current ratio and th......
Q:
Draw the three different trees with five nodes, and the six different trees with six nodes. Repeat the problem for rooted trees. For this problem the order of the branches of a rooted tree is...
A:
Sure I can solve the problem in the image in detail Part a Rooted tree A rooted tree is a tree in which one vertex has been designated as the root and......
Q:
Washington, Inc., makes three models of motorized carts for vacation resorts, X-10, X-20, and X-40. Washington manufactures the carts in two assembly departments: Department A and Department B. All...
A:
Required solution Requirement A Calculation of unit cost of each model transferred to finished goods Product Unit Material cost See Note 1 Unit Cost D......
Q:
A telephone communication system is set up at a company where 125 executives are employed. The system is initialized by the president, who calls her four vice presidents. Each vice president then...
A:
Model the problem with a complete quaternary tree rooted at the......
Q:
(a) Consider the subgraph of G (in Fig. 12.54) induced by the vertices a, b, c, d. This graph is called a kite. How many nonidentical (though some may be isomorphic) spanning trees are there for this...
A:
a There are nonidentical though some are isomorphic spanning trees for the kite induced by a b c d S......
Q:
Suppose that you work at AllRoad Parts and Kelly tells you that she doesnt believe that cheap, elastic provisioning of servers is possible. There has to be a catch somewhere, she says. Write a...
A:
The cloud is based on the Internet as its foundation It also utilizes a design philosophy called the......
Q:
1-800-Flowers.com is a leading online retailer of flowers and gifts. The company moved from telephone to online ordering in the mid-1990s. Since then, it has grown to over $1 billion in revenue and...
A:
1 Providing a better customer experience is necessary today because customer expectations have risen significantly in the digital age With the ease of comparing products and services online customers......
Q:
At the next big family gathering, you want to impress your grandparents with the innovative ideas you have learned in business school. They have decades of experience in investing in the stock market...
A:
Ladies and gentlemen I d like to share with you an innovative approach to business that I ve been learning about in business schoola triple bottom line approach I understand that many of you have a we......
Q:
Recall a meeting that you recently had, such as a team presentation of a case analysis. What were your impressions of what happened in the planning of the presentation and how things like the...
A:
I recently had a meeting with my team to plan a presentation of a case analysis We were assigned the case of a company that was struggling to compete......
Q:
Strong language? Nudity? Stereotypes? They are all represented in the ads you will review for this AdForum exercise. Why do advertisers court controversy by producing potentially disturbing,...
A:
Here are my ratings of the ads for this segment on a scale of offensiveness where 1 not at all offensive and 10 extremely offensive Ad 1 7 10 This ad is offensive because it uses strong language and s......
Q:
Research leading to the development of a scramjet engine is worthwhile. Commercial aircraft incorporating such an engine could cross the Pacific in as little as two hours. This would relieve the...
A:
let s construct argument patterns for the provided statements 1 Research leading to the development......
Q:
For the plane stress element shown in Figure P15 -15 subjected to a uniform temperature rise of T = 50°F, determine the thermal force matrix {fT}. Let E = 30 Ã 106 psi, v = 0.3, a = 7.0...
A:
i y j y m 0 4 4 i x m x j 0......
Q:
Refer to the table to answer the following questions. Year Nominal GDP (in billions) Total Federal Spending (in billions) Real GDP (in billions) Real Federal Spending (in billions) 2000 9,817 578...
A:
Answer a i Federal Spending in 2013 Federal Spending in 2000......
Q:
You've seen that the power of a product property allows you to rewrite (a b)n as an bn. Is there a power of a sum property that allows you to rewrite (a + b)n as an + bn? Write some numerical...
A:
Sample result a b n is not neces......
Q:
Consider this sequence: 72, 72. 25, 72. 5, 72. 75, 73 a. Use your calculator to evaluate each term in the sequence. If answers are not exact, approximate to four decimal places. b. Find the...
A:
a 49 79 7023 129 6418 210 8723 343 b 30 7023 49 9395 81 2305 132 1277 The sequence......
Q:
For 9a-d, graph the equations on your calculator. a. y = x2 b. y = x3 c. y = x4 d. y = x5 e. How do the graphs compare? How do they contrast? What points (if any) do they have in common? f. Predict...
A:
AD 4 7 4 7 1 6 2 6 2 1 e Sample answer As the exponents increase t......
College Accounting, Chapters 1- 15 23rd Edition - ISBN: 0357391942 - Free Book