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Chapter 14: Problem 60

What is a path in a graph?

Short Answer

Expert verified
A path in a graph is a sequence of vertices where each adjacent pair is connected by an edge. The length of a path is the number of edges in it.

Step by step solution

01

Understand the Concept of a Path

A path in a graph is a sequence of vertices where each adjacent pair is connected by an edge. In other words, a path is a way to go from one vertex (or 'node') to another, moving along the edges of the graph.
02

Visualize the Path

Usually, paths are easier to understand when visualized. Let's say we have a graph with 5 vertices labeled A, B, C, D, and E. If there are edges connecting A-B, B-C, C-D, and D-E, then a path from A to E would involve moving from A to B, B to C, C to D, and finally, D to E.
03

Understand Path Length

The length of a path is the number of edges in it. For example, in the path described above (A-B-C-D-E), the length of the path would be 4, because there are 4 edges along the path.

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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?

Why is the Brute Force Method impractical for large numbers of vertices?

What is a graph? Define vertices and edges as part of your description.

In Exercises 49-52, draw a graph with the given characteristics. The graph has four odd vertices and at least one loop.

In Exercises 13-18, a connected graph is described. Determine whether the graph has an Euler path (but not an Euler circuit), an Euler circuit, or neither an Euler path nor an Euler circuit. Explain your answer. The graph has 78 even vertices and two odd vertices.
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