Networks Terminology 1 - Year 12

What is the key characteristic of a walk in graph theory?

• No edges are repeated

• No vertices are repeated

• Edges can be repeated

• Vertices can be repeated but not edges

Which of the following is true about a trail?

• Edges can be repeated

• No edges are repeated, but vertices can be repeated

• Neither edges nor vertices can be repeated

• Both edges and vertices can be repeated

In a path, which of the following must be true?

• No edges or vertices are repeated

• Edges can be repeated, but vertices cannot

• Vertices can be repeated, but edges cannot

• Both edges and vertices are repeated

Which of the following best describes the relationship between a circuit and a cycle?

• Every cycle is a circuit, but not every circuit is a cycle

• Every circuit is a cycle, but not every cycle is a circuit

• A cycle and a circuit are the same

• Neither cycles nor circuits can repeat vertices

What is the difference between an Eulerian trail and an Eulerian circuit?

• A) An Eulerian trail repeats vertices, while an Eulerian circuit does not.

• B) An Eulerian circuit starts and ends at the same vertex, while an Eulerian trail does not.

• C) An Eulerian trail follows every edge, while an Eulerian circuit does not.

• D) An Eulerian circuit repeats edges, while an Eulerian trail does not.

What is a Hamiltonian path?

• A) A path that visits every edge exactly once.

• B) A path that visits every vertex exactly once without repeating any edges.

• C) A path that starts and ends at the same vertex.

• D) A path that covers all vertices and edges.

Which of the following statements is true about a Hamiltonian cycle?

• A) It visits every edge exactly once.

• B) It visits every vertex exactly once and returns to the starting vertex.

• C) It does not need to visit every vertex.

• D) It must visit every edge of the graph.

Which of the following conditions is required for a graph to have a Hamiltonian path?

• The graph must be connected, and all vertices must have an even degree.

• The graph must have exactly two vertices of odd degree.

• The path must visit every vertex exactly once without repeating any edges.

• The path must visit every edge exactly once.

Which type of graph structure would NOT contain an Eulerian circuit?

• A connected graph where all vertices have an even degree.

• A connected graph with exactly two vertices of odd degree.

• A connected graph with at least one vertex of odd degree.

• A complete graph where all vertices have the same degree.

Every cycle is a circuit, but not every circuit is a:

• Cycle

• Path

• Trail

• Circuit