/*! 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 57 What is meant by the degree of a... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 14: Problem 57

What is meant by the degree of a graph's vertex and how is it determined?

Short Answer

Expert verified
The degree of a vertex in a graph is the number of edges connected to it. In an undirected graph, count the number of edges meeting at the vertex. For directed graphs, distinguish between incoming (in-degree) and outgoing (out-degree) edges. A loop counts as two edges.

Step by step solution

01

Definition of Vertex Degree

In graph theory, a vertex (or a node) is one of the fundamental units from which graphs are formed. The degree of a vertex in a graph is the number of edges that are incident on it.
02

Undirected Vs Directed Graphs

In an undirected graph, the degree of a vertex is simply the number of edges connecting to it. However, in a directed graph, we distinguish between the 'in-degree' and the 'out-degree'. The 'in-degree' of a vertex refers to the number of incoming edges, while the 'out-degree' refers to the number of outgoing edges.
03

Counting Edges to Determine Degree

To determine the degree of a vertex, count the number of edges that meet at that vertex. In the case of a loop, it is counted twice.

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

Make Sense? In Exercises 60-63, determine whether each statement makes sense or does not make sense, and explain your reasoning. A complete graph has 120 distinct Hamilton circuits. How many vertices does the graph have?

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, is connected, and every edge is a bridge.

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

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

Make Sense? In Exercises 60-63, determine whether each statement makes sense or does not make sense, and explain your reasoning. I'm amazed by the power of my new computer, so this evening I plan to use it to find an optimal Hamilton circuit for a complete, weighted graph with 20 vertices.
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

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.