a. Draw an acyclic graph with 7 vertices and 4 components. b. Prove that if G is an acyclic graph with u vertices and 4 components, each of which is a tree, that G has u - 4 edges. c. Draw a graph with 7 vertices and 6 edges that is not a tree.

a. Draw an acyclic graph with 7 vertices and 4 components. b. Prove that if G is an acyclic graph with u vertices and 4 components, each of which is a tree, that G has u - 4 edges. c. Draw a graph with 7 vertices and 6 edges that is not a tree.

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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Concept explainers

Depth First Search

Depth-first search (DFS) also known as Depth First traversal is an algorithm used to traverse or search the nodes in a tree or graph data structure. Traversal usually means visiting all the nodes of a graph. DFS performs in a depth-ward manner. It uses a stack to remember the vertices it has visited. The search starts from the root node, where any arbitrary node is selected as a root node in a graph, and then each node is explored along each branch before performing backtracking. The DFS algorithm uses a recursive technique by following the idea of backtracking. DFS algorithm does this by performing an in-depth search of all the nodes by traversing in a forward direction. If the required node is not found, it starts backtracking to previously visited nodes.

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a. Draw an acyclic graph with 7 vertices and 4 components.
b. Prove that if G is an acyclic graph with u vertices and 4 components, each of which is a tree, that G
has u - 4 edges.
c. Draw a graph with 7 vertices and 6 edges that is not a tree.
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