Networks and graphs Quiz

1. A network has five edges. What is the sum of the degrees of its vertices?

• A. 5
• B. 10
• C. 12
• D. 20

2. In a weighted network of road distances, how is the length of a route found?

• A. Count the vertices visited
• B. Count the edges used
• C. Take the largest edge weight
• D. Add the weights of the edges used

3. Row $X$ of an adjacency matrix is $\begin{pmatrix}0&1&1&0&1\end{pmatrix}$. What is the degree of $X$?

• A. 3
• B. 2
• C. 5
• D. 1

4. A connected network has exactly two vertices of odd degree. Which statement is true?

• A. It has an Euler circuit
• B. It has no Euler route at all
• C. It has an Euler trail that starts at one odd vertex and ends at the other
• D. It must have a Hamiltonian cycle

5. What does a Hamiltonian path do?

• A. Uses every edge exactly once
• B. Visits every vertex exactly once
• C. Always returns to the start
• D. Finds the shortest route