Graph Theory — Learn free

Self-check

Questions 1–10 of 10

1. What is graph theory?
Question 1A. A mathematical framework for representing, analysing and solving problems involving interconnected dataB. A technique for drawing bar chartsC. A method for compressing image filesD. A spreadsheet formula languageE. A style of database indexing used only in finance
2. Which of the following is NOT listed as a field where graph theory is applied?
Question 2A. Social networks, to analyse relationships and influenceB. Cooking, to combine recipe ingredientsC. Biology, to map genetic networks and protein interactionsD. Transportation, to improve route planning and traffic flowE. Project management, to visualise tasks and dependencies
3. In the three-city example of graph theory, where A is connected to B and B is connected to C, what is the degree of vertex B?
Question 3A. 0B. 1C. 2D. 3E. 5
4. Graph theory groups its tools under three headings. Which set is correct?
Question 4A. Tables, rows and columnsB. Input, process and outputC. Nodes, weights and coloursD. Properties, structures and relationshipsE. Ingestion, transformation and serving
5. What real-world analogy is used for a directed graph (digraph) in graph theory?
Question 5A. Cities on a mapB. Two-way roadsC. Bus stopsD. Distances in kilometresE. One-way streets
6. In the three-city graph, what happens to connectivity if vertex B is removed?
Question 6A. A and C will no longer be connectedB. A and C become directly connectedC. The graph gains a cycleD. The degree of A increases to 2E. Nothing changes
7. In graph theory, what is a path?
Question 7A. The weight assigned to an edgeB. A sequence that shows how to move from one vertex to anotherC. A vertex with the highest degreeD. The removal of a vertex from a graphE. A pair of vertices that are not connected
8. If an edge from C back to A is added to the graph A to B to C, what is formed?
Question 8A. A bipartite graphB. A disconnected graphC. A cycle: A to B to C to AD. A treeE. A weighted graph
9. When is a graph described as connected?
Question 9A. When every edge carries a weightB. When it has at least one cycleC. When all edges have a directionD. When there is a path between every pair of verticesE. When it has exactly three vertices
10. In the school bus analogy for graph theory, with Stop 1 to Stop 2 being 2 km and Stop 2 to Stop 3 being 3 km, what do the vertices, edges and weights represent, and how long is the path from Stop 1 to Stop 3?
Question 10A. Vertices are roads, edges are stops, weights are times; the path is 6 kmB. Vertices are pupils, edges are timetables, weights are fares; the path is 2 kmC. Vertices are buses, edges are drivers, weights are speeds; the path is 3 kmD. Vertices are stops, edges are roads, weights are distances; the path is 1 kmE. Vertices are bus stops, edges are roads between stops, weights are distances; the path is 5 km