Consider the following graph: ![0 (graph_1.-png) 1. Write down the adjacency matrix and adjacency lists specifying this graph. (Assume that the matrix rows and columns and vertices in the adjacency lists follow in the alphabetical order of the vertex labels.) 2. Starting at vertex `a' order, traverse the graph by depth-first search and construct the corresponding depth-first search tree. Give the order in which the vertices were reached for the first time (pushed onto the traversal stack) and the order in which the vertices became dead ends (popped off the stack). and resolving ties by the vertex alphabetical

Consider the following graph: ![0 (graph_1.-png) 1. Write down the adjacency matrix and adjacency lists specifying this graph. (Assume that the matrix rows and columns and vertices in the adjacency lists follow in the alphabetical order of the vertex labels.) 2. Starting at vertex `a' order, traverse the graph by depth-first search and construct the corresponding depth-first search tree. Give the order in which the vertices were reached for the first time (pushed onto the traversal stack) and the order in which the vertices became dead ends (popped off the stack). and resolving ties by the vertex alphabetical

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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How many entries would the adjacency list representation for the following graph contain? (Assume that the array slots for each vertex count as one entry, and the linked list nodes for edges each count as one entry as well.) D B E A F G
Discussion:1. Depth-first search (DFS) is a technique that is used to traverse a tree or a graph.DSF technique starts with a root node and then traverses the adjacent nodes ofthe root node by going deeper into the graph. In the DFS technique, the nodes aretraversed depth-wise until there are no more children to explore.- Once we reach the leaf node (no more child nodes), the DFS backtracks andstarts with other nodes and carries out traversal n a similar manner. DFStechnique uses a stack data structure to store the nodes that are beingtraversed. DFS Technique (Depth-First Traversal)o Following is the algorithm for the DFS technique.o Algorithm:1. Start with the root node and insert it into the stack2. Pop the item from the stack and insert into the ‘visited’ list3. For the node marked as ‘visited’ (or in visited list), add the adjacent nodesof this node that are not yet marked visited to the stack.4. Repeat steps 2 and 3 until the stack is empty.
Algorithm Answer as soon as possible ?
For the following graph: 4 (a) Determine the order of vertices traversed by depth-first search (with lower index as priority in case of ambiguity) and show how the stack would look when running it. (b) Compute the discovery and finishing times (DFS numbers) for each vertex. (c) What edges make up the DFS tree or forest? Classify the rest of the edges. (d) Determine whether there is a cycle or not in this graph. If there is not, give a possible topological ordering.
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4-Clique Problem The clique problem is to find cliques in a graph. A clique is a set of vertices that are all adjacent - connected - to each other. A 4-clique is a set of 4 vertices that are all connected to each other. So in this example of the 4-Clique Problem, we have a 7-vertex graph. A brute-force algorithm has searched every possible combination of 4 vertices and found a set that forms a clique: https://en.wikipedia.org/wiki/Clique_problem You should read the Wikipedia page for the Clique Problem (and then read wider if need be) if you need to understand more about it. Note that the Clique Problem is NP-Complete and therefore when the graph size is large a deterministic search is impractical. That makes it an ideal candidate for an evolutionary search. For this assignment you must suppose that you have been tasked to implement the 4-clique problem as an evolutionary algorithm for any graph with any number of vertices (an n-vertex graph). The algorithm succeeds if it finds a…
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1) There is undirected graph below. Please give traversal results of BFS and DFS respectively, assuming start from vertex G.< Undirected ↓ G A D B C F E
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Breadth First Search can be modi ed to solve the problem: • Assume that you are given an undirected, weighted(connected) graph G = (V;E) as shown below, • You need to nd the length of the shortest path from v to each other vertex in G.
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