Practice Paths and cycles with authentic MYP MYP Extended Mathematics exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like core principles, advanced applications, and practical problem-solving. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of MYP examiners.
A delivery driver starts at vertex , visits vertices , , and in order, and then returns to vertex . No vertex is repeated, except for the start and end vertex. Which specific term describes this route?
A connected graph contains at least one vertex with a degree of . Which of the following statements about must be true?
In a connected graph with vertices, the existence of an articulation point (cut vertex) makes a Hamiltonian cycle impossible. Why is this the case?
A vertex whose removal increases the number of connected components in a graph is called a ______. The existence of such a vertex makes a Hamiltonian cycle impossible because any such cycle would have to pass through that vertex more than once.
Which of the following statements correctly describes the relationship between a path and a cycle in a simple graph?
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 , and , how many distinct ways are there to pair these vertices to find the minimum weight to add?
The 'enter-leave pairing' principle explains traversability. According to this logic, why must the start and end vertices of an Eulerian trail (which is not a circuit) have odd degrees?
In the Chinese Postman Problem, if a connected weighted graph has exactly odd vertices, what is the minimum number of shortest paths between pairs of these vertices that must be duplicated to make the graph Eulerian?
A connected graph has exactly odd-degree vertices. To create a graph that contains an Eulerian trail (but not an Eulerian circuit), the minimum number of shortest paths between pairs of odd vertices that must be duplicated is
Practice Paths and cycles with authentic MYP MYP Extended Mathematics exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like core principles, advanced applications, and practical problem-solving. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of MYP examiners.
A delivery driver starts at vertex , visits vertices , , and in order, and then returns to vertex . No vertex is repeated, except for the start and end vertex. Which specific term describes this route?
A connected graph contains at least one vertex with a degree of . Which of the following statements about must be true?
In a connected graph with vertices, the existence of an articulation point (cut vertex) makes a Hamiltonian cycle impossible. Why is this the case?
A vertex whose removal increases the number of connected components in a graph is called a ______. The existence of such a vertex makes a Hamiltonian cycle impossible because any such cycle would have to pass through that vertex more than once.
Which of the following statements correctly describes the relationship between a path and a cycle in a simple graph?
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 , and , how many distinct ways are there to pair these vertices to find the minimum weight to add?
The 'enter-leave pairing' principle explains traversability. According to this logic, why must the start and end vertices of an Eulerian trail (which is not a circuit) have odd degrees?
In the Chinese Postman Problem, if a connected weighted graph has exactly odd vertices, what is the minimum number of shortest paths between pairs of these vertices that must be duplicated to make the graph Eulerian?
A connected graph has exactly odd-degree vertices. To create a graph that contains an Eulerian trail (but not an Eulerian circuit), the minimum number of shortest paths between pairs of odd vertices that must be duplicated is