16. Use the flow graph of K; to answer the following questions. a 6/6 9/11 3/4 6/6 3/3 3/3 2/2 8/8 1/1 b K2 a. Identify each edge and the capacity in graph K, Enter your answer in the space below the question. For example: c(s, a) = 4 b. What is the flow into vertex a and the flow out of a? Flow into a = Flow out of a = c. What is the flow into vertex c and the flow out of c? Flow into c= Flow out of c= d. What is the flow out of source s and the flow into r? Flow into s= Flow out of t=

16. Use the flow graph of K; to answer the following questions. a 6/6 9/11 3/4 6/6 3/3 3/3 2/2 8/8 1/1 b K2 a. Identify each edge and the capacity in graph K, Enter your answer in the space below the question. For example: c(s, a) = 4 b. What is the flow into vertex a and the flow out of a? Flow into a = Flow out of a = c. What is the flow into vertex c and the flow out of c? Flow into c= Flow out of c= d. What is the flow out of source s and the flow into r? Flow into s= Flow out of t=

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Similar questions

Let DIST (u, v) denote the distance between vertex u and v. It is well known that distances in graphs satisfy the triangle inequality. That is, for any three vertices u, v, w, DIST (u, v) ≤ DIST (u, w) + DIST (w, v). Let D∗ denote the distance between the two farthest nodes in G. Show that for any vertex s D∗ ≤ 2 max DIST (s, v).
The following table presents the implementation of Dijkstra's algorithm on the evaluated graph G with 8 vertices. a) What do the marks (0, {a}) and (∞, {x}) in the 1st row of the table mean? b) What do the marks marked in blue in the table mean? c) Reconstruct all edges of the graph G resulting from the first 5 rows of the table of Dijkstra's algorithm. d) How many different shortest paths exist in the graph G between the vertices a and g?
Run BFS algorithm on the following graph starting with vertex s. Whenever there is a choice of vertices, choose the one that is alphabetically first. What is the order that the vertices are visited? What is the shortest path from vertex s to vertex b?
3. From the graph above determine the vertex sequence of the shortest path connecting the following pairs of vertex and give each length: a. V & W b. U & Y c. U & X d. S & V e. S & Z 4. For each pair of vertex in no. 3 give the vertex sequence of the longest path connecting them that repeat no edges. Is there a longest path connecting them?
2. Let G = (V, E) be a directed weighted graph with the vertices V = {A, B, C, D, E, F) and the edges E= {(A, B, 12), (A, D, 17), (B, C, 8), (B, D, 13), (B, E, 15), (B, F, 13), (C, E, 12), (C, F, 25)}, where the third components is the cost. (a) Write down the adjacency list representation the graph G = (V, E).
Suppose that G is an unconnected graph that consists of 4 connected components. The first component is K4, the second is K2,2, the third is C4 and the fourth is a single vertex. Your job is to show how to add edges to G so that the graph has an Euler tour. Justify that your solution is the minimum number of edges added.
a) Illustrate the sequence of vertices of this graph visited using depth-first search traversal starting at vertex g. b) Illustrate adjacency list representation and adjacency matrix representation, respectively, for this graph. What are the advantages and disadvantages of those two representations? c) Describe an algorithm to find in the graph a path illustrated below that goes through every edge exactly once in each direction.
2. Consider the graph G2(V2, E2) below. 2a. Find the MST of this graph with Kruskal’s algorithm. Draw the MST, and show the table [edge] [w(u, v)] [mark]. 2b. Find the MST of this graph with Prim’s algorithm starting at vertex 'a'. Draw the MST and list the vertices in order you added them to the MST. 2c. Would you get a different MST if you repeat 2b starting at vertex 'e'? Why or why not?
Consider the graph depicted below. Answer the following questions: What is the degree of vertex a? What is the sum of degrees of all vertices? Who are the neighbors of vertex f? [Please, give the list in alphabetical order, separating letters with only a comma. Do not insert blank spaces] How many zeros does the adjacency matrix of the graph above contain? What is the value on row g and column d of the adjacency matrix?
Answer True or False to the following claims: a. If G is graph on at most 5 vertices and every vertex has degree 2, then G is a cycle. b. Let G be a forest. If we add an edge to G, then G is no longer a forest. c. Let G be a graph, and let u, v, and w be vertices in G. Suppose that a shortest path from u to v in G is of length 3, andsuppose that a shortest path from v to w in G is of length 4. Then a shortest path from u to w in G is of length 7.
2. Q1) You are given an undirected connected planar graph. There are 10 vertices and 7 faces in the graph. What is the number of edges in the graph? Note that: A graph is said to be planar if it can be drawn in a plane so that no edge cross. Q2) In how many ways can we pick any number of balls from a pack of three different balls? Q3) The distance between 2 points A and B is 1320Km. Two cars start moving towards each other with 50 Km/hr and 60 Km/hr. After how many hours do they meet?
Let G be a graph with 7 vertices, where eachvertex is labelled by a number from 1 to 7. Twovertices are selected at random. Let us call themu and v. Now, directed edges are drawn from u toall other vertices except v and directed edges aredrawn from all vertices to v except from u. Let xbe the total possible topological sortings of G.hint: You may remember the terms factorials orfibonacci?Write down the value of x: