Question: Let G = (V, E) be a directed graph. A black hole is a vertex v ? V such that all vertices u v have

Let G = (V, E) be a directed graph. A black hole is a vertex v ? V such that

all vertices u Let G = (V, E) be a directed graph. A black hole v have an outgoing edge (u, v) leading to v

and v has no outgoing edge.

(a) Prove or disprove: in a directed graph, there is at most one black hole.

(b) Design an algorithm which can detect whether or not there is a black hole in a directed graph. Your score on this question will depend on how efficient your algorithm is. You must describe your algorithm in plain English (no pseudocode). You must clearly state what graph representation you are working with (adjacency matrix or adjacency lists). You must give the running time of your algorithm and explain why you get this running time. Maximum one page.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Databases Questions!

Let G = (V, E) be a directed graph. A black hole is a vertex v ? V such that all vertices u v have an outgoing edge (u, v) leading to v and v has no outgoing edge. (a) Prove or disprove: in a...

1. Let G (V, E) be a directed graph. A black hole is a vertex v E V such that all vertices uu have an outgoing edge (u, u) leading to u . and v has no outgoing edge. (a) Design an algorithm which can...

Let G = (V, E) be a directed graph. A black hole is a vertex u E V such . all vertices u u have an outgoing edge (u,v) leading to v and v has no outgoing edge. (a) Prove or disprove: i a directed...

Let G - (V, E) be a directed graph. A black hole is a vertex v EV such . all vertices uu have an outgoing edge (u,v) leading to u . and v has no outgoing edge. (a) Design an algorithm which can...

Let G = (V, E) be a directed graph where V = {1, 2, , n}. Given a vertex v let Sv denote the set of vertices that have a path from v (excluding v), and let Tv be the set of vertices from which there...

3 Max-Flow and Graph Reliability (35 pts] Let G = (V, E) be a directed graph with two specified vertices st EV. Assume that contains at least one s-t path. A subset of edges E' CE is a separating...

Asymptotic Analysis Homework 2.03 Let G = (V, E) be a directed graph with n vertices and m edges. It is known that in dfsTrace of G the function dfs is called n times, once for each vertex. It is...

Let G = (V, E) be a directed graph where V = { 1,2, . . . ,n} such that n is odd; Le n = 2k+1 for some k > 0. Given a vertex v, let TO, be the set of all vertices from which there is path to v. Let...

Let G = (V, E) be a directed graph with weight function w : E R, and let n = |V|. We define the mean weight of a cycle c = e 1 , e 2 , . . . , e k of edges in E to be Let * = min c (c), where c...

4. [10 pts (U) Consider the following claims. i. Is the following claim true or false? "For every directed graph G (V, E) with positive integer capacities and for every pair of vertices s and t...

Mr. Boyba is a mixed income earner. In year 2020, he earned gross compensation income of P1,887,880, including 13th month pay and other benefits of P138,000. In his trading business, his gross sales...

How should the fixed costs of a service department be charged to operating departments?

What is the AIR (the simple rate) on the loan? The AIR is 208%. (Assume that there are exactly 52 weeks in a year.)What is the effective annual rate (the right thing) on the loan? Again assume that...

Compared with half a century ago, adoption has become _ _ _ _ _ _ _ _ _ common, but it is more open and acceptabl e , so we probably discuss it _ _ _ _ _ _ _ . fill in the blanks more or much less or...

b. What are its goals and objectives?

3. Messages of affect and value will decrease. Ambiguity in interpreting information will increase. Managers will have to seek new ways of communicating the affective component of messages.

6. Expectations of work performance may be machine driven. Employees in some organizations will perceive this as dehumanizing and coercive. (pp. 480481)