**Task: Draw an undirected graph, if possible (if not possible, explain why not), that meets the following criteria:**a. Five vertices, three edges, and is connected.b. Five vertices, three edges, and two connected components.c. Five vertices, two edges, and three connected components.d. Five vertices, two edges, and two connected components.e. Five vertices, six edges, and two connected components.---**Explanations:**a. **Graph is possible**: A connected graph with five vertices and three edges can be made by having, for example, a path between four of the vertices, with the fifth vertex connected to any one of them.b. **Graph is possible**: This graph can be made by creating a triangle with three edges (one component) and leaving two vertices isolated, or connecting them via a single edge (second component).c. **Graph is not possible**: With only two edges, you cannot create three separate connected components. Each edge creates a connection between two vertices, so having three components would require at least three edges.d. **Graph is possible**: A simple example would be to connect two pairs of vertices with one edge each, leaving the fifth vertex isolated.e. **Graph is not possible**: With five vertices and six edges, the graph must form a complete graph where all vertices are connected (which is a single component), violating the condition of having two connected components.

“Since you have posted a question with multiple sub-parts, we will solve the first three sub- parts…

Draw an undirected graph, if possible (if not possible explain why not that has a. Five vertices and three edges and is connected. b. Five vertices, three edges, and two connected components. c. Five vertices, two edges, and three connected components.

Draw an undirected graph, if possible (if not possible explain why not that has a. Five vertices and three edges and is connected. b. Five vertices, three edges, and two connected components. c. Five vertices, two edges, and three connected components.

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

Eight puzzle problem

The N-puzzle problem contains N tiles (N+1 including empty tiles) where the value of N can be 8, 15, 24, etc. The puzzle is divided into the square root of (N+1) rows and the square root of (N+1) columns. These problems have an initial state or configuration and a goal state or configuration. The puzzle can be solved by shifting the tiles one by one in the empty space. The objective is to place the numbers on the tiles to match the final state using the empty space. The other name for the N-puzzle problem is the sliding puzzle.

Question

**Task: Draw an undirected graph, if possible (if not possible, explain why not), that meets the following criteria:**

a. Five vertices, three edges, and is connected.

b. Five vertices, three edges, and two connected components.

c. Five vertices, two edges, and three connected components.

d. Five vertices, two edges, and two connected components.

e. Five vertices, six edges, and two connected components.

---

**Explanations:**

a. **Graph is possible**: A connected graph with five vertices and three edges can be made by having, for example, a path between four of the vertices, with the fifth vertex connected to any one of them.

b. **Graph is possible**: This graph can be made by creating a triangle with three edges (one component) and leaving two vertices isolated, or connecting them via a single edge (second component).

c. **Graph is not possible**: With only two edges, you cannot create three separate connected components. Each edge creates a connection between two vertices, so having three components would require at least three edges.

d. **Graph is possible**: A simple example would be to connect two pairs of vertices with one edge each, leaving the fifth vertex isolated.

e. **Graph is not possible**: With five vertices and six edges, the graph must form a complete graph where all vertices are connected (which is a single component), violating the condition of having two connected components.

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