State the definition of a path in regard to graph theory.
For each of the following graphs, state a valid path:
List all valid paths:
Determine the number of unique paths from B \text{ to } D without passing over the same vertex twice.
Determine the number of unique paths from A to D, without passing over the same node more than once.
For each of the following networks, state a valid walk that crosses each vertex once:
State a path that satisfies the given information for each of the following networks:
The path starts at B and ends at X.
The path starts at H, goes through 4 other vertices, and then ends at B.
The path starts at Q, has length 3, and ends at P.
The path starts at P and ends at Q
Consider the given network:
State whether the following are valid walks:
K, F, P, K
K, P, F, K, P
K, P, F, R, M
R, P, F, M, R
K, P, F, K
F, R, M, P, F
State whether the following are valid paths:
K, P, F, R, M
K, P, F, K, P
K, P, F, K
Define the following terms in relation to graph theory:
Loop
Connected graph
Bridge
Cycle
For each of the following lists, select the odd one out and explain your choice:
Walk
Path
Cycle
Trail
Path
Closed walk
Cycle
Closed trail
State whether each of the following graphs is connected:
For each of the following networks, state a valid circuit:
For each network, state which of the highlighted edges in the network is a bridge:
Consider the following graph:
How many edges are connected to vertex A?
List the vertices adjacent to vertex E.
State the vertex directly connected to all other vertices.
Which vertex is not directly connected to vertex A?
Consider the following graph:
Which vertex is isolated?
How many edges are there in the network?
How many vertices are there?
Which vertex is the loop connected to?
State whether the following networks are traversable:
For the networks below, which vertices can you start at in order to traverse the network?
A team of workers is to repair seven bridges that cross the river running through town, as shown in the image below:
After repairing each bridge (which involves crossing the bridge), the workers close it off for 24 hours.
Given that they start in the bottom-left area of the town (where the truck is in the image), can the workers repair all seven bridges in one day without going back over a closed bridge?
After repairing all seven bridges, which road do the workers leave by: top left, bottom left, top right or bottom right?