/*! 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 28 How do you determine whether or ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 28

How do you determine whether or not a graph is traversable?

Short Answer

Expert verified
A graph is traversable if all vertices have an even degree (Eulerian graph), or if there are exactly two vertices with odd degrees (semi-Eulerian); start at one odd-degree vertex and end at the other. In cases where more than two vertices have odd degrees, the graph is not traversable.

Step by step solution

01

Understand traversability

A graph is called traversable if it is possible to navigate through the graph, visiting each edge exactly once. This is linked to the property of Eulerian graphs (named after Leonard Euler), which are graphs where each vertex has an even degree.
02

Calculate the degree of vertices

To determine whether a graph is traversable you should determine the degree of each vertex. The degree of a vertex is the number of edges that are incident to (or meet at) that vertex. This can be done by examining the graph and counting the number of edges that each vertex has.
03

Determine traversability

A graph is traversable if all vertices in the graph have an even degree (Eulerian graph). However, if exactly two vertices have odd degrees and the rest have even degrees, the graph is semi-Eulerian, meaning it is traversable but one must start at one of the odd-degree vertices and end at the other. If more than two vertices have odd degrees, the graph is not traversable.

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

Which one of the following is a better buy: a large pizza with a 14 -inch diameter for \(\$ 12\) or a medium pizza with a 7 -inch diameter for \(\$ 5\) ?

Although the Eiffel Tower in Paris is not a solid pyramid, its shape approximates that of a pyramid with a square base measuring 120 feet on a side and a height of 980 feet. If it were a solid pyramid, what would be the Eiffel Tower's volume, in cubic yards?

The rungs of a ladder are perpendicular to each side, so the rungs are parallel to each other.

What general assumption did Euclid make about a point and a line in order to prove that the sum of the measures of the angles of a triangle is \(180^{\circ}\) ?

Describe each type of angle: acute, right, obtuse, and straight.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Decision Maths

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.