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Chapter 14: Problem 62

What is a connected graph?

Short Answer

Expert verified
A connected graph is a graph where there is a path from any point to any other point in the graph.

Step by step solution

01

Definition

A connected graph is a type of graph in which there is a path from any point to any other point in the graph. In other words, there's a pathway connecting every pair of vertices.
02

Further Clarification

In a connected graph, you can choose any two vertices and you can find at least one path that connects the two. This path may lead directly from one vertex to another, or it may pass through other vertices.
03

Example

To give an example, imagine a graph with four vertices A, B, C, and D. If vertices A and B are connected, B and C are connected, and C and D are connected, then the graph is a connected graph. This is because there is a path from any vertex to any other vertex.

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Most popular questions from this chapter

If a graph is given, how do you determine whether or not it is a tree?

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.

Describe how to determine the number of Hamilton circuits in a complete graph.

What is an Euler path?

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