A subset of the nodes of a graph G is a dominating set if every other node

Question:

A subset of the nodes of a graph G is a dominating set if every other node of G is adjacent to some node in the subset. Let

DOMINATING-SET = {〈G, k〉| G has a dominating set with k nodes}.

Show that it is NP-complete by giving a reduction from VERTEX-COVER.

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

Step by Step Answer:

Related Book For book-img-for-question

Introduction to the theory of computation

ISBN: 978-0470530658

3rd edition

Authors: Michael Sipser

See More Books

Question Posted: Sep 02, 2020 05:00 AM

See More Questions

Let HALF-CLIQUE = {G| G is an undirected graph having a complete subgraph with at least m/2 nodes, where m is the number of nodes in G}. Show that HALF-CLIQUE is NP-complete.
A planar graph is a graph that can be drawn in a plane without any two edges intersecting. a. Show that neither of the graphs in Figure 9.87 is planar. b. Show that in a planar graph, there must...
Define SUBGRAPH-ISOMORPHISM as the problem that takes a graph, G, and another graph, H, and determines if H is isomorphic to a subgraph of G. That is, the problem is to determine whether there is a...
Builder Products, Incorporated, uses the weighted-average method in its process costing system. It manufactures a caulking compound that goes through three processing stages prior to completion....
What is the cutoff number of heads above which you reject the null hypothesis at the = 0.05 significance level? A coin is flipped 10 times and comes up heads 9 times. You have reason to suspect...
*32.7 Donald is domiciled, resident and ordinarily resident in the UK. He has the following income in 2009-10: UK trading profits 38,175 UK bank interest (net amount) 1,600 Income from foreign...
How do each of the following influence inventory decisions? a. Lumpy demand. b. Minimum orders. c. Transportation costs. d. Multiples. LO.1
Suppose Bill is on a low-carbohydrate diet. He can eat only three foods: Rice Krispies, cottage cheese, and popcorn. The marginal utilities for each food are tabulated below. Bill is allowed only 167...
Which of the following is a motive for a leveraged buyout? Multiple Choice To force firms with surplus cash to distribute it to shareholders The opportunity to create better incentives for managers...
The Cheesecake Factory Incorporated (NASDAQ: CAKE) was started by Evelyn Overton when she sold cheesecakes from her basement in Detroit in the 1940s. Its first restaurant opened in Beverly Hills in...
Recall, in our discussion of the ChurchTuring thesis, that we introduced the language D = {p| p is a polynomial in several variables having an integral root}. We stated, but didnt prove, that D is...
Show that the following problem is NP-complete. You are given a set of states Q = {q 0 , q 1 , . . . , q l } and a collection of pairs {(s 1 , r 1 ), . . . , (s k , r k )} where the s i are distinct...
a. Construct a relative frequency table for the weights of regular Pepsi. Use bins of 0.8130-0.8179 0.8180-0.8229 0.8230-0.8279 0.8280-0.8329 0.8330-0.8379 0.8380-0.8429 b. Construct a cumulative...
On Apple company with specific iPhone product Required to conduct a SWOT and PESTEL analysis, identifying the internal strengths and weaknesses and external opportunities and threats of the Apple...
In which social platforms are Walmart's brand/company active? In your opinion, are they doing a good job regarding customer engagement through social media channels? (Required: screenshots from the...
After you have watched both films, how would you describe each film? Also, consider what makes these early films different. List as many observations as you can that separate the Lumi re brothers...
How to develop the following points with the Poshmark application for second hand? 1. What are the main reasons for using this product? Or why not? 2. What are the hidden motivations? 3. Are there...
Suppose, in an experiment to determine the amount of sodium hypochlorite in bleach, you titrated a 22.84 mL sample of 0.0100 M K I O 3 with a solution of N a 2 S 2 O 3 of unknown concentration. The...
Write the decimal value of the following hexadecimal numbers: a. 234 16 b. 112D 16
The electric field due to a line charge is given by where l is a constant. Show that E is solenoidal. Show that it is also conservative. E =
Recall the two FEC schemes for VoIP described in Section 9.3. Suppose the first scheme generates a redundant chunk for every four original chunks. Suppose the second scheme uses a low-bit rate...
How arc different RTP streams in different sessions identified by a receiver? How are different streams from within the same session identified?
Consider the figure below (which is similar to Figure 9.3). A sender begins sending packetized audio periodically at t = 1. The first packet arrives at the receiver at t = 8. Figure 9.3 a. What are...
Fig 1. Rolling a 4 on a D4 A four sided die (D4), shaped like a pyramid (or tetrahedron), has 4 flat surfaces opposite four corner points. A number (1, 2, 3, or 4) appears close to the edge of each...
I just need help with question #4 please! Thank you! Windsor Manufacturing uses MRP to schedule its production. Below is the Bill of Material (BOM) for Product A. The quantity needed of the part...
(25) Suppose that we have an economy consisting of two farmers, Cornelius and Wheaton, who unsurprisingly farm corn c and wheat w, respectively. Assume that both farmers produce their crop of choice...

A subset of the nodes of a graph G is a dominating set if every other node

Question:

Step by Step Answer:

To show that DOMINATINGSET is NPcomplete we need to show that it is in NP and that it is NPhard To show that DOMINATINGSET is in NP we need to show th...View the full answer

Introduction to the theory of computation

Students also viewed these Computer science questions