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Chapter 10: Problem 27

What does it mean if a graph is traversable?

Short Answer

Expert verified
A graph is traversable if you can visit every vertex or node exactly once without lifting your pencil from the paper, provided the graph is connected and the degree of every vertex is even.

Step by step solution

01

Understanding Graphs

A Graph is a non-linear data structure consisting of nodes or vertices(V) and edges(E) connecting these nodes. An Edge represents a path between two Nodes or a way for one Node to associate with another. Nodes/Vertex are entities in a graph.
02

Definition of Traversability

In Graph theory, a graph is said to be traversable if it is possible to visit each vertex or node exactly once without having to lift your pencil from the paper. This concept is also known as a path or a walk in the graph.
03

Conditions for a graph to be Traversable

A graph is traversable if and only if it is connected and the degree of every vertex is even. The degree of a vertex refers to the number of edges incident to it. If these conditions are not met, the graph will not be traversable.

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