Assume that all the graphs in the fol- lowing problems are simple, with no self-loops or...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Assume that all the graphs in the fol- lowing problems are simple, with no self-loops or multiple edges (in the same direction) between any two vertices. (a) Show that the total number of edges for a connected undirected graph with n vertices is bounded between n - 1 and (2), i.e., n-1≤m≤ (2) (b) Show that the total number of edges for a strongly connected directed graph with n vertices is bounded between n and n(n-1). (Hint: If we remove the directions, n - 1 suffices. Why having n - 1 edges isn't sufficient to ensure strong connectivity in a directed graph?) (c) Given a graph with n vertices and edge set E as the input, write the pseudocode of algorithms that achieve the following tasks: i. Assuming E is the adjacency linked list of undirected edges, given a vertex s, return the list of vertices that are reachable from s. This is called the connected component of s. ii. Let's refer to the function from the previous part as Connected Comp. Now, write an algo- rithm that returns the set of edges required to make your graph connected. The algorithm should also minimize the number of edges returned, and its time complexity should be O(m +n). Assume that all the graphs in the fol- lowing problems are simple, with no self-loops or multiple edges (in the same direction) between any two vertices. (a) Show that the total number of edges for a connected undirected graph with n vertices is bounded between n - 1 and (2), i.e., n-1≤m≤ (2) (b) Show that the total number of edges for a strongly connected directed graph with n vertices is bounded between n and n(n-1). (Hint: If we remove the directions, n - 1 suffices. Why having n - 1 edges isn't sufficient to ensure strong connectivity in a directed graph?) (c) Given a graph with n vertices and edge set E as the input, write the pseudocode of algorithms that achieve the following tasks: i. Assuming E is the adjacency linked list of undirected edges, given a vertex s, return the list of vertices that are reachable from s. This is called the connected component of s. ii. Let's refer to the function from the previous part as Connected Comp. Now, write an algo- rithm that returns the set of edges required to make your graph connected. The algorithm should also minimize the number of edges returned, and its time complexity should be O(m +n).
Expert Answer:
Answer rating: 100% (QA)
a i For a connected undirected graph with n vertices the minimum numb... View the full answer
Related Book For
Posted Date:
Students also viewed these programming questions
-
Our company - Public Eye Corp. - is an early-stage company providing real-time access to satellite images. Our clients include government entities and private firms. Demand for our services has been...
-
An appropriate structure for large-scale distributed systems is as multiple, independently administered, firewall-protected, domains. Examples are a national health service, a national police service...
-
The information listed below refers to the employees of Lemonica Company for the year ended December 31, 2016. The wages are separated into the quarters in which they were paid to the individual...
-
Review Organicos financial statements presented in the chapter for the month ended March 31, 2017. Review the balance sheet and determine the business form Hailey Walker has chosen to organize her...
-
Adler owes Panessi, a police captain, $5,000. Adler threatens that unless Panessidischarges him from the debt, Adler will disclose the fact that Panessihas on several occasions become highly...
-
Analogous to the conventional partial property M i , one can define a constant-T, V partial property M i : Show that M i and M i are related by the equation: Demonstrate that the M i satisfy a...
-
The efficiency ratio measures the relation between outputs from and inputs to a process. According to the WBCSD, a company wanting to become eco-efficient should strive to: 1.Reduce the material...
-
Assume that Stillwater Designs produces two automotive subwoofers: S12L7 and S12L5. The S12L7 sells for $475, and the S12L5 sells for $300. Projected sales (number of speakers) for the coming five...
-
If I buy 364 units per year at a cost of C = $4 each, H is 25% * C, S is $10, and the order size Q = 91. What is my total annual cost, TC?
-
How would the legal realists (e.g., Karl Llewellyn and Oliver Wendell Holmes) view the current relationship between social psychology and the law?
-
Rundle Airline Company is considering expanding its territory. The company has the opportunity to purchase one of two different used airplanes. The first airplane is expected to cost $15,660,000; it...
-
A soccer player kicks the ball with an initial velocity of 22.3 m/s [14 degrees above the horizontal] on a level playing field. Determine the soccer balls: a) total hang time b) maximum height...
-
1What will be the maturity value of a promissory note subscribed today for 150,000 at an interest rate of 27.5% if the term of the operation is 10 months? 2.What will be the maturity value of a...
-
On January 1, 2025, Sheridan Company had a balance of $410,400 of goodwill on its balance sheet that resulted from the purchase of a small business in a prior year. The goodwill had an indefinite...
-
[-12 -2] Reduce the matrix 1 2 1 to the upper triangular form by using elementary transformations. 1-1 0
-
What ethical considerations arise in the context of organizational culture, particularly regarding issues of inclusivity, equity, and social responsibility, and how can organizations align their...
-
? solve the cauchy problem, -gu + xuy -(1) with and! 4(21,0) sinac for.
-
7 A 29-year-old, previously healthy man suddenly collapses at a party where legal and illicit drugs are being used. Enroute to the hospital, he requires resuscitation with defibrillation to establish...
-
During 2016, Jake Gore worked for two different employers. Until May, he worked for Wonderman Construction Company in Kansas City, Kansas, and earned $21,500. The state unemployment rate for...
-
Gabrielle Hunter, a waitress at the Hole-in-the-Wall restaurant, worked 42 hours this week and collected over $500 in tips. The restaurant uses the full tip credit against the minimum wage and pays...
-
The taxable wages and withheld taxes for Stafford Company (EIN 00-0001462), semiweekly depositor, for the first quarter of 2016 follow. a. Complete Schedule B of Form 941 for the first quarter for...
-
Analytical procedures: a. Are intended to detect material misstatements in financial statement accounts. b. Are concerned with how internal control policies or procedures are applied. c. Are...
-
Substantive tests of details: a. Are intended to detect material misstatements in financial statement accounts. b. Are concerned with how internal control policies or procedures are applied. c. Are...
-
Tests of controls: a. Are intended to detect material misstatements in financial statement accounts. b. Are concerned with how internal control policies or procedures are applied. c. Are evaluations...
Study smarter with the SolutionInn App