/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 12 Draw the graph with the given ad... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 12

Draw the graph with the given adjacency matrix.

Short Answer

Expert verified
Given the adjacency matrix, identify the connected vertices by examining the non-zero elements in the matrix. Draw vertices as points labeled by their number, and connect the identified connected vertices with lines. If the graph is weighted, label each edge with its weight. Ensure the resulting graph matches the adjacency matrix by checking the connections between vertices.

Step by step solution

01

Understand the adjacency matrix

The adjacency matrix is a square matrix, where its rows and columns represent the vertices of the graph. The value at the (i, j) position in the matrix indicates the weight of the edge between vertices i and j. In case of an unweighted graph, the value will be 1 if there is an edge between vertices i and j and 0 otherwise.
02

Identify the connected vertices

To determine which vertices are connected by an edge, examine each element of the adjacency matrix. If the value of the (i, j) element is non-zero, it means there is an edge between vertices i and j. Record these pairs of vertices for the next step.
03

Draw the vertices and edges

Begin by drawing the vertices of the graph. You can represent each vertex by a point, labelled by its number. Next, refer to the list of connected vertices generated in step 2. Draw a line between each pair of connected vertices. In case of a weighted graph, label the edge with its weight.
04

Check the resulting graph

After drawing the graph, compare it with the given adjacency matrix. Ensure that all vertices are properly connected according to the adjacency matrix, by re-checking the non-zero values of the matrix. If everything matches, it's complete. If there are inconsistencies, revise the graph accordingly. Throughout the process, refer to the given adjacency matrix as needed to ensure that the graph accurately reflects the connections specified by the matrix.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Determine if each complete bipartite graph \(K_{m, n}\) is Hamiltonian. If a graph is not Hamiltonian, does it contain a Hamiltonian path? $$K_{3,3}$$

Is the complete graph \(K_{n}\) regular? If so, find its degree.

Determine if each complete bipartite graph \(K_{m, n}\) is Hamiltonian. If a graph is not Hamiltonian, does it contain a Hamiltonian path? $$K_{3,4}$$

Let \(v_{1}, \ldots, v_{n}\) be n vertices with degrees \(\operatorname{deg}\left(v_{1}\right), \ldots, \operatorname{deg}\left(v_{n}\right),\) respectively, such that \(\sum_{i=1}^{n} \operatorname{deg}\left(v_{i}\right)\) is even. Prove that there exists a graph satisfying these conditions. [Hint: Let \(\sum_{i=1}^{n} \operatorname{deg}\left(v_{i}\right)=2 e .\) Use induction on e. \(]\)

Let \(G\) be the union of two simple disconnected subgraphs \(H_{1}\) and \(H_{2}\) with chromatic numbers \(m\) and \(n,\) respectively. What can you say about the chromatic number \(c\) of \(G ?\)
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.