MYP Extended Mathematics Topic 11.2 Paths and Cycles…

The Chinese Postman Problem is defined as finding the shortest 'closed' route that traverses every edge at least once. What does the term 'closed' specifically signify in this context?

In the context of the Chinese Postman Problem, if a connected weighted graph has 4 odd-degree vertices $A, B, C$ , and $D$ , how many distinct ways are there to pair these vertices to find the minimum weight to add?

A connected graph represents a series of hallways in a museum. The degrees of the vertices (junctions) are given by the set $\{2, 4, 4, 6, 2, 4\}$ . Which of the following statements is true about this graph?

A trail on a connected graph passes through a specific vertex $V$ four times (entering and leaving each time). If $V$ is not the start or the end of the trail, and no edges are repeated, what is the minimum degree that vertex $V$ must have?

Based on the 'unpaired sock' analogy for traversability, what does a vertex with an even degree represent in terms of a journey through the network?

The route cannot repeat any vertices

The route must form a Hamiltonian cycle

The graph must not have any external connections

The route must start and end at the same vertex

The graph has an Eulerian circuit.

The graph has an Eulerian trail but no Eulerian circuit.

The graph has exactly two odd vertices.

The graph is non-traversable.

A location where you can enter and leave without getting stuck

The mandatory starting point of the journey

A dead end in the network

A vertex that cannot be part of a Hamiltonian cycle

MYP Extended Mathematics 11.2 Paths and Cycles Questionbank

MYP Extended Mathematics 11.2 Paths and Cycles Questionbank

MYP Extended Mathematics 11.2 Paths and Cycles Questionbank

MYP Extended Mathematics 11.2 Paths and Cycles Questionbank

MYP MYP Extended Mathematics Topic 11.2 Paths and Cycles Questionbank