Does the following bipartite graph contain a matching that covers L? L R b 3 d g Yes, because it is degree-constrained. Yes, because it is not degree-constrained. No, because it is degree-constrained. No, because it is not degree-constrained. It is not possible to determine this based on the provided graph.

Does the following bipartite graph contain a matching that covers L? L R b 3 d g Yes, because it is degree-constrained. Yes, because it is not degree-constrained. No, because it is degree-constrained. No, because it is not degree-constrained. It is not possible to determine this based on the provided graph.

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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It was claimed that anyone involved in the Hollywood film industry can be linked through their film roles to Kevin Bacon within six steps. You are suspicious of such a claim and decide to verify it using the given dataset.Before you start to verify the claim, you first notice that it is not possible for this claim to be true if the actor graph is not even connected. Briefly explain how you can verify a given undirected graph is connected (i.e there exists a path between any two actors in the graph). Include the runtime of your algorithm as well.
Please list the bottleneck edges in the attached graph.
Draw the weighted graph represented by the following adjacency matrix. I'm a bit confused on how to finish the weighted graph since on the 5th and 6th row, there is a 2. And could you also confirm the rest of my graph is correct?
Given N cities represented as vertices V₁, V2, un on an undirected graph (i.e., each edge can be traversed in both directions). The graph is fully-connected where the edge eij connecting any two vertices vį and vj is the straight-line distance between these two cities. We want to search for the shortest path from v₁ (the source) to VN (the destination). ... Assume that all edges have different values, and €₁,7 has the largest value among the edges. That is, the source and destination have the largest straight-line distance. Compare the lists of explored vertices when we run the uniform-cost search and the A* search for this problem. Hint: The straight-line distance is the shortest path between any two cities. If you do not know how to start, try to run the algorithms by hand on some small cases first; but remember to make sure your graphs satisfy the conditions in the question.
How many edges does a graph have if its degree sequence is 2, 4, 4, 5, 3?A. Draw a graph with the above listed sequence.B. Is it possible to draw an Euler Circuit with such a sequence of vertex degrees?Is it possible to draw an Euler Path? If yes, to either of these questions, draw the a graph that supports your answer.
An Euler path, in a graph or multigraph, is a walk through the graph which uses every edge exactly once. An Euler circuit is an Euler path which starts and stops at the same vertex. NOTE: graphs are in the image attached. Which of the graphs below have Euler paths? Which have Euler circuits? List the degrees of each vertex of the graphs above. Is there a connection between degrees and the existence of Euler paths and circuits? Is it possible for a graph with a degree 1 vertex to have an Euler circuit? If so, draw one. If not, explain why not. What about an Euler path? What if every vertex of the graph has degree 2. Is there an Euler path? An Euler circuit? Draw some graphs. Below is part of a graph. Even though you can only see some of the vertices, can you deduce whether the graph will have an Euler path or circuit? NOTE: graphs is in the image attached.
For each course at a university, there may be one or more other courses that are its prerequisites. How can a graph be used to model these courses and which courses are prerequisites for which courses? Should edges be directed or undirected? Looking at the graph model, how can we find courses that do not have any prerequisites and how can we find courses that are not the prerequisite for any other courses?
Given N cities represented as vertices V₁, V2,..., UN on an undirected graph (i.e., each edge can be traversed in both directions). The graph is fully-connected where the edge eij connecting any two vertices v; and vj is the straight-line distance between these two cities. We want to search for the shortest path from v₁ (the source) to VN (the destination). Assume that all edges have different values, and e₁, has the largest value among the edges. That is, the source and destination have the largest straight-line distance. Compare the lists of explored vertices when we run the uniform-cost search and the A* search for this problem. Hint: The straight-line distance is the shortest path between any two cities. If you do not know how to start, try to run the algorithms by hand on some small cases first; but remember to make sure your graphs satisfy the conditions in the question.
This assignment requires the extension of your graph code to apply it to movement through a “world”. The world will be a weighted, directed graph, with nodes for the start position and target(s), and other nodes containing blocks, diversions, boosts and portals. For example, in a cat world, a dog may block you, toys may take your attention, food may give you more energy and portals may prove that cats are pan-dimensional beings. This structure could also be used to implement Snakes and Ladders, or other games. Your task is to build a representation of the world and explore the possible routes through the world and rank them. Sample input files will be available – with various scenarios in a cat world. Your program should be called gameofcatz.py/java, and have three starting options: * No command line arguments : provides usage information * "-i" : interactive testing environment * "-s" : simulation mode (usage: gameofcatz –s infile savefile) When the program starts in interactive mode,…
I would like to know how to make an undirected graph implementation and how to make a method to find the connectivity between two Nodes assuming the graph is pre-processed ->what is the least amount of time. to check the connection between two nodes?
Question 4 Given a undirected weighted graph G associate a number which is the weight of the heaviest edge in the tree. Find the spanning tree whose number is minimum among all spanning trees. Explain. (Hint: this involves a simple observation. The question is how to justify this observation. There are many ways to justify. The easiest is probably to recall where "exponentiation" appeared in the HW and use it.) (E,V). With each spanning tree we
Question 2 What is the shortest path between A and Z in the graph below? (The length of a path is the sum of the numbers along the edges on the path.) Explain briefly how you have found this solution: what algorithm or solution strategy did you use? Does it work on any graph? Path (e.g., A-B-E-Z) : A- - Z Explanation : E 1 G 2 2 1 3 A 3 3 2 3 B 4 1 F 2.