/*! 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 61 What is a circuit? Describe the ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 14: Problem 61

What is a circuit? Describe the difference between a path and a circuit.

Short Answer

Expert verified
A circuit is a closed trail in a graph where the only repeated vertices are the start and end vertices. A path, however, is a sequence of edges in a graph connecting two vertices, with no vertices being repeated in the sequence. The key difference is that the path does not allow the repeating of vertices except for the beginning and end points if it becomes a circuit.

Step by step solution

01

Define a Circuit

In graph theory, a circuit is a closed trail where the only repeated vertices are the start and end vertices. A trail is simply a walk in the graph that doesn't reuse any edges but possibly reuses vertices. An illustration or example can aid in understanding this concept.
02

Define a Path

On the other hand, a path in a graph is a sequence of edges that connects two vertices with no vertices being repeated in the sequence. Essentially, a path is a trail in a graph involving no repeated vertices except possibly for the first and final vertices if the path forms a circuit. Again, an example will help illuminate this.
03

Point out the Differences

The essential difference between a path and a circuit lies in the fact that a path doesn't reuse any vertices, apart from perhaps the beginning and end vertices, whereas a circuit, being a closed trail, may reuse vertices, but the start and end vertices must be the same.

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

What is a complete graph?

. What is a Hamilton circuit? How does this differ from an Euler circuit?

In Exercises 11-16, a graph with no loops or more than one edge between any two vertices is described. Which one of the following applies to the description? i. The described graph is a tree. ii. The described graph is not a tree. iii. The described graph may or may not be a tree. The graph has five vertices and four edges.

Although the Nearest Neighbor Method does not always give the Hamilton circuit for which the sum of the weights is a minimum, Kruskal's Algorithm always gives the spanning tree with the smallest possible total weight.

Describe a practical example of a traveling salesperson problem other than those involving one-way airfares or distances between errand locations.
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Logic and Functions

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.