PartialQuestion 4In breadth-first search (BFS) of graph G (unweighted), if there exists an edge (x, y) in G,then which of the following statements is correct?(1) node y is in the node x's adjacency list.(2) (x.y) can be a BFS tree edge.(3) (x.y) cannot be a forward edge.(4) y.d must be at most x.d+1(5) node x must be in the queue at the same time or before node y is in the queue.(6) If (x.y) is in shortest path from the source node to node y, (x.y) must be in some BFStree.(1)(2)O (3)O (4)O (5)(6)

Answered: Question 4 In breadth-first search…

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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4. Consider the graph G, shown below, which is simply a copy of K5. 02 V3 5 V1 24 V5 How many distinct spanning trees does G have? (Hint: Break up your search by the isomorphism type of the tree, as discovered on the previous page. So for example, start by counting the paths of length 5 in G. Then proceed to the next type of tree with 5 vertices. The total number of trees is 125, but please use this answer only to check that your solution is complete!)
15
Let G = (V, E) be an undirected graph and each edge e ∈ E is associated with a positive weight ℓ(e).For simplicity we assume weights are distinct. Is the following statement true or false? Let T be a minimum spanning tree for the graph with the original weight. Suppose we replace eachedge weight ℓ(e) with ℓ(e)^2, then T is still a minimum spanning tree.
Question2 and 3 plz！ will give a like
Please show step-by-step explanations. Thank you. About the Petersen Graph, (a) The Petersen Graph P is shown below. Assign an edge weight of 1 to each edge of P. Use either Kruskal or Prim’s Algorithm to find a (necessarily minimum weight)spanning-tree of P. you must be clear about whichthe algorithm you choose and show and explain each step leading to the spanning tree.
You are given a weighted tree T.(As a reminder, a tree T is a graph that is connected and contains no cycle.) Each node of the tree T has a weight, denoted by w(v). You want to select a subset of tree nodes, such that weight of the selected nodes is maximized, and if a node is selected, then none of its neighbors are selected.
Question 4: Suppose you had a road network represented as a connected graph (vertices are intersections and edges are roads between intersections). How can you determine if closing a set of intersections results in the inability to travel between some remaining pair of intersections? Note: If an intersection is closed, all edges touching that vertex are closed too. You may assume we already know about depth first search, breadth first search, minimum spanning tree algorithms, and the shortest path algorithm from class, but you can’t assume anything else from class.
Question 6 The worst-case run-time to change the priority of a heap element is: A. (nlogn) B. 0(n) C. 0(1) D. 0(logn) Ε. Θ(n2) Question 7 Consider a maximum heap, represented by an array: 52, 42, 32, 22, 27, 28, 29, 20, and 16. Now consider that a value 47 is inserted into this heap. What is the new heap after the insertion? A. 52, 42, 32, 22, 27, 28, 29, 20, 16, 47 B. 52, 47, 32, 42, 27, 28, 29, 22, 16, 20 C. 52, 42, 32, 22, 47, 28, 29, 20, 16, 27 D. 52, 47, 32, 22, 42, 28, 29, 20, 16, 27 E. 52, 47, 32, 42, 27, 28, 29, 22, 20, 16 Question 8 The output of an in-order traversal of a binary tree is 1,2,3,4,5,6, and the output of pre- order traversal of the same binary tree is 6,1,4,2,3,5. What is the output of the post-order traversal of the same binary tree? A. 3,1,4,5,2,6 B. 3,2,4,5,1,6 C. 3,2,5,4,1,6 D. 1,2,4,6,5,3 E. 3,2,5,1,4,6 Question 9 Given an array A storing n elements. Which one of the following statements is true? A. Heap sort is always the slowest algorithm in practice to…
Trouble arises if G is a directed, linked graph. When an edge is removed from a graph, it might be considered a bridge. Every bridge e must be an edge in the depth-first search tree of G. Please include an example or two to illustrate your point.
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Let Tsp be the tree of shortest paths of the below graph (G1) starting from vertex A and let TMST be a minimum spanning tree of (G1). Circle the only assertion that is FALSE 24 18. A 14 19 30 15 20 16 Both Tsp and TMST Contain the two edges of weight 6 Tsp and TMST have the same number of edges O Tsp and TMST have six edges in common The shortest path between A and H uses exactly 4 edges
2. A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected, edge-weighted undirected graph that connects all the vertices together, without any cycles and with the minimum possible total edge weight. There are 2 very popular algorthms to calcualte MSTs of a graph. These algorithms are Kruskal's algorithm and Prim's algorithm. Figure 2: A weighted graph and its minimum spanning tree (ii) Can a Minimum Spanning Tree finding algorithm like Prim's algorithms be used to find out the Maximum Spanning Tree? If yes, then explain your steps. If not, explain why not with logic.

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