Prove the following. If in a graph any two vertices are connected by a unique path, the

Question:

Prove the following.
If in a graph any two vertices are connected by a unique path, the graph is a tree.

Data from Prob. 14

Prove the following.
The path connecting any two vertices u and v in a tree is unique.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Advanced Engineering Mathematics

ISBN: 978-0470458365

10th edition

Authors: Erwin Kreyszig

See More Books

Question Posted: Jun 17, 2022 03:16 AM

See More Questions

Ticket to Ride is a popular board game that involves connecting cities in a given railroad network. In this assignment you will prototype some potential approaches for creating an AI player for this...
If G = (V, E) is a loop-free connected undirected graph and a, b V, then we define the distance from a to b (or from b to a), denoted d(a, b), as the length of a shortest path (in G) connecting a and...
Let G = (V, E) be an undirected, connected graph with weight function w : E R, and suppose that |E| |V| and all edge weights are distinct. A second-best minimum spanning tree is defined as follows....
In figure, one end of a uniform beam weighing 20 x V3N is attached to a wall with a hinge. The other end is supported by a wire connected to the wall as shown. If the tension in the wire is a x 10N,...
Outline the reasons why a business may wish to adopt e-commerce.
For four years, Mary Nations invested $4,000 each year in America Bank stock. The stock was selling for $34 in 2010, for $48 in 2011, for $37 in 2012, and $52 in 2013. a. What is Mary's total...
Calculate the equilibrium constant at $25^{\circ} \mathrm{C}$ for the following reaction: \[ \mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{~g}) ightarrow 2 \mathrm{NO}_{2}(\mathrm{~g}) \] Given that...
Accounts and Notes Payable the following are selected 2010 transactions of Darby Corporation. Sept. 1 Purchased inventory from Orion Company on account for $50,000. Darby records purchases gross and...
Troy Engines, Limited, manufactures a variety of engines for use in heavy equipment. The company has always produced all of the necessary parts for its engines, including all of the carburetors. An...
Determine the maximum speed for each car if the normal acceleration is limited to 0.88g. The roadway is unbanked and level. 21 m 16 m Problem 2/100
Sketch the graph for the given adjacency matrix. 0 1 0 1 1 0 1 0 0 1 0 0 0 0 0
Find flow augmenting paths: 2) Co 4, 2 10,3 3, 1 (2) 5,3 6,0 (3) 8,5 1, 1 5
What is the ABAs position on what confidentiality duty is owed a prospective client?
True Or False One criticism of punitive damages is that they lead to excessive litigation by plaintiffs who hope to intimidate defendants into settling.
A _________ is a document absolving a defendant of all liability.
Explain the criticism that in a tort system all of society should bear the brunt of the increase of plaintiff injury awards.
True Or False An increase in tort filings points to a clear increase in litigiousness.
A typical Mary Carter agreement a. involves no exchange of funds, even on paper, before trial. b. provides that the plaintiff cannot agree to settle with the nonagreeing defendant for an amount less...
If the operation in Problem 9.66 were per-formed on an electrical-discharge machine, what would be the estimated machining time?
What can scientists learn by comparing the fossilized skeletons of extinct primates with the bones of modern species?
An article in the Journal of Applied Physiology [Humidity Does Not Affect Central Nervous System Oxygen Toxicity (2001, Vol. 91, pp. 13271333)] reported that central nervous system (CNS) oxygen...
An article in the Journal of Human Nutrition and Dietetics [The Validation of Energy and Protein Intakes by Doubly Labeled Water and 24-Hour Urinary Nitrogen Excretion in Post-Obese Subjects (1995,...
The confidence interval for a population proportion depends on the central limit theorem. A common rule of thumb is that to use the normal approximation for the sampling distribution for p, you...
Provide an analysis of the benefits and challenges of having a growth mindset as opposed to having a fixed mindset. Examine the benefits of each type of mindset, as well as the challenges that each...
Discuss and explain what is Performance Management (P M)? How does P M fit into corporate strategy? What's in it for me? How does it work? What are my responsibilities? How does PM relate to other...
A conducting spherical shell has inner radius 2 / 3 R and outer radius R . ( a ) Suppose we put a charge Q onthe shell ( a conductor ) so that all of the charge goes to the outer radius. Find the...

Prove the following. If in a graph any two vertices are connected by a unique path, the

Question:

Step by Step Answer:

A tree is a special type of graph in which there exists only one ...View the full answer

Advanced Engineering Mathematics

Students also viewed these Mathematics questions