Consider the following edge-weighted graph G with 9 vertices and 16 edges: 90 Q6.1 Kruskal 0 40 50 80 130 110 70 150 60 30 10 120 140 20 100 List the weights of the MST edges in the order that Kruskal's algorithm adds them to the MST. Your answer should be a sequence of 8 integers, with one space between each integer

Consider the following edge-weighted graph G with 9 vertices and 16 edges: 90 Q6.1 Kruskal 0 40 50 80 130 110 70 150 60 30 10 120 140 20 100 List the weights of the MST edges in the order that Kruskal's algorithm adds them to the MST. Your answer should be a sequence of 8 integers, with one space between each integer

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

See similar textbooks

Similar questions

Consider an undirected graph on 8 vertices, with 12 edges given as shown below: Q2.1 Give the result of running Kruskal's algorithm on this edge sequence (specify the order in which the edges are selected). Q2.2 For the same graph, exhibit a cut that certifies that the edge ry is in the minimum spanning tree. Your answer should be in the form E(S, V/S) for some vertex set S. Specifically, you should find S.
Let G = (X ∪ Y, E) be a bipartite graph such that the vertices are partitioned into two groups Xand Y , and each edge has one end point in X and one end point in Y .A 2-1 generalized matching is a set of edges S ⊂ E satisfying the following two conditions:1. Every vertex in X belongs to at most two edges in S.2. Every vertex in Y belongs to at most one edge in S.Give an algorithm to find the size (number of edges) of maximum 2-1 generalized matching
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).
How many undirected graphs (not necessarily connected) can be constructed out of a given set V= {V 1, V 2,…V n} of n vertices ? Group of answer choices 2^(n(n-1)/2) 2^n n(n-l)/2 n! Which of the following is an advantage of adjacency list representation over adjacency matrix representation of a graph? Adding a vertex in adjacency list representation is easier than adjacency matrix representation. In adjacency list representation, space is saved for sparse graphs. DFS and BSF can be done in O(V + E) time for adjacency list representation. These operations take O(V^2) time in adjacency matrix representation. Here is V and E are number of vertices and edges respectively. All of the above Given the starting vertex A, what is the visit order of the graph shown in Fig. 1 under the DFS traversal algorithm. ABDCFE ACBDFE ABCDFE ADBCEF Assume you have the adjacency matrix representing a graph. 1 represents a connection while -1 represents a lack of one:[-1, 1, - 1][-1, -1, 1][1, -1,…
Discrete mathematics. Let G = (V, E) be a simple graph4 with n = |V| vertices, and let A be its adjacency matrix of dimension n × n. We want to count the L-cycles : such a cycle, denoted by C = u0u1 · · · uL with uL = u0 contains L distinct vertices u0, . . . , uL-1 et L edges E(C) = {uiui+1 | 0 ≤ i ≤ L − 1} ⊆ E. Two cycles are distinct if the edge sets are different : C = C' if and only if E(C) = E(C'). We define the matrices D, T, Q, the powers of A by matrix multiplication : D = A · A = A2, T = A · D = A3, Q = A · T = A4. Consider the values on the diagonals. Prove that the number of 3-cycles N3 in the whole graph is N3 = 1/6 ∑ u∈V Tu,u
Discrete mathematics. Let G = (V, E) be a simple graph4 with n = |V| vertices, and let A be its adjacency matrix of dimension n × n. We want to count the L-cycles : such a cycle, denoted by C = u0u1 · · · uL with uL = u0 contains L distinct vertices u0, . . . , uL-1 et L edges E(C) = {uiui+1 | 0 ≤ i ≤ L − 1} ⊆ E. Two cycles are distinct if the edge sets are different : C = C' if and only if E(C) = E(C'). We define the matrices D, T, Q, the powers of A by matrix multiplication : D = A · A = A2, T = A · D = A3, Q = A · T = A4. Consider the values on the diagonals. Prove that for any vertex u ∈ V with degree d(u), d(u) = Du,u.
Let G be a connected graph with n vertices and m edges.Which of the following statements are true?(i) G is a tree if and only if n = m+1.(ii) G is a tree if and only if m = n+1.(iii) G is a tree if and only if the addition of any edgeto G will produce a unique cycle.(iv) G is a tree if and only if G contains at least onepath b etween any two vertices.(v) If G is connected, then G is a tree if and only if Gcontains at most one path between any two vertices.(vi) A connected subgraph of a tree is always a tree.
Given an undirected, weighted graph G(V, E) with n vertices and m edges, design an (O(m + n)) algorithm to compute a graph G1 (V, E1 ) on the same set of vertices, where E1 subset of E and E1 contains the k edges with the smallest edge weights , where k < m.
Consider the following graph. If we run breadth first search on this graph starting at any vertex, which one of the following is a possible order for visiting the nodes? NQMPOR QMNPOR MNOPQR QMNPRO Assume the following adjacency list for a graph. After you draw the graph, what is the path to reach D from A. Vertex Edges A --------> B, C B --------> C C --------> B, E D --------> B E --------> B, D Both (B) and (C) A->B->C->E->D A->B->C->D A->C->E->D
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?
Given a vertex set W = {1, 2, 3, 4}, solve for the following questions: (i) Knowing that edges are the same if and only if they have the same endpoint, how many different edges are possible? (ii) Suppose for this question that graphs are different if they have different sets of edges (they do not depend on if the graphs are isomorphic or not). How many simple graphs are there with the vertex set W? (iii) Draw the eleven nonisomorphic simple graphs that have four vertices.
Suppose you have the 6-vertex directed graph G=(V,E), with V={a,b,c,d,e,f} and E={(a,c),(c,b),(e,d)}. What is K(G)? 1 4 3 2