Computer Science · Graph Theory

Consider the following statements regarding the structural rules of graph traversal: I. A trail is a walk in which vertices are permitted to repeat, but the repetition of edges is strictly prohibited. II. In a path, the strict prohibition on vertex repetition automatically ensures that edges cannot be repeated. III. A circuit is a walk that starts and ends at the same vertex and explicitly allows the repetition of edges. IV. A cycle is a closed path that prohibits vertex repetition except for the start and end vertices, and it must have a minimum length of 3. Which of the statements given above are correct?