What is a path in graph terminology?

What is a path in graph terminology?

• A. A walk with repeated edges
• B. A walk with no repeated edges or vertices
• C. A walk that visits all vertices exactly once
• D. A closed trail

Answer: (B)

In graph theory, a path is defined as a sequence of edges that connect a sequence of distinct vertices without retracing any steps. This means that in a path, each vertex is visited exactly once, which prevents any repetitions of both edges and vertices. This definition aligns perfectly with the selected answer, highlighting the essential characteristic of a path: it must be free of repetitions. To clarify further, a walk can include repeated edges and vertices, but a path is more restrictive as it disallows such repetitions, making it a key concept in understanding how vertices and edges interact in a graph. Understanding this concept is crucial for various applications in graph theory, such as in networking and connected systems.

In graph theory, a path is defined as a sequence of edges that connect a sequence of distinct vertices without retracing any steps. This means that in a path, each vertex is visited exactly once, which prevents any repetitions of both edges and vertices. This definition aligns perfectly with the selected answer, highlighting the essential characteristic of a path: it must be free of repetitions.

To clarify further, a walk can include repeated edges and vertices, but a path is more restrictive as it disallows such repetitions, making it a key concept in understanding how vertices and edges interact in a graph. Understanding this concept is crucial for various applications in graph theory, such as in networking and connected systems.