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Graph theory - Quiz
Contributed by: Leigh
  • 1. Graph theory is a branch of mathematics that deals with the study of graphs, which are mathematical structures used to model relationships between objects. A graph consists of a set of vertices, or nodes, which are connected by edges, or links. Graph theory has applications in various fields such as computer science, social network analysis, and operational research. It helps in solving problems related to connectivity, routing, optimization, and more. Overall, graph theory provides a powerful framework for analyzing and understanding complex systems and relationships.

    What is a graph in graph theory?
A) A chart or diagram
B) A mathematical structure consisting of vertices and edges
C) A pie chart
D) A line graph
  • 2. What is a vertex in a graph?
A) A line connecting two points in a graph
B) A point or node in a graph
C) A function in graph theory
D) A path between two vertices
  • 3. What is an edge in a graph?
A) A node's color in a graph
B) A connection between two vertices
C) A vertex with no connections
D) A loop on a vertex
  • 4. What is a path in graph theory?
A) An isolated vertex
B) A sequence of edges that connect a sequence of vertices
C) A cycle in a graph
D) A disconnected graph
  • 5. In a simple graph, can an edge connect a vertex to itself?
A) No
B) Sometimes
C) Depends on the number of vertices
D) Yes
  • 6. What is the degree of a vertex in a graph?
A) The number of vertices in the graph
B) The number of edges incident to the vertex
C) The size of the graph
D) The distance from one vertex to another
  • 7. What is a planar graph?
A) A multigraph
B) A disconnected graph
C) A graph that can be drawn on a plane without any edge intersections
D) A graph with cycles
  • 8. What is a weighted graph?
A) An undirected graph
B) A graph with only one vertex
C) A graph in which a number (weight) is assigned to each edge
D) A graph with maximum number of edges
  • 9. What is an isomorphism between two graphs?
A) The same number of vertices in both graphs
B) A loop on a vertex in both graphs
C) A bijection between their vertex sets that preserves edges
D) Two disconnected graphs
  • 10. What was the title of Leonhard Euler's paper that is considered the first in graph theory?
A) Solutio Problematis ad Geometriam Situs Pertinentis
B) On the Nature of Graphs
C) Graph Theory and its Applications
D) The Seven Bridges of Königsberg
  • 11. What type of graph allows edges to connect a vertex to itself?
A) Multigraph
B) Simple graph
C) Directed graph
D) Undirected graph
  • 12. Who introduced the term 'graph' in the context of mathematics?
A) Arthur Cayley
B) Dénes Kőnig
C) Leonhard Euler
D) James Joseph Sylvester
  • 13. Which problem in graph theory involves coloring regions of a map with four colors such that no two adjacent regions share the same color?
A) Seven Bridges problem
B) Four-color problem
C) Knight's tour problem
D) Graph connectivity problem
  • 14. Who first posed the four-color problem?
A) Francis Guthrie
B) Peter Tait
C) Augustus De Morgan
D) William Rowan Hamilton
  • 15. Who donated all royalties from their textbook on graph theory to fund the Pólya Prize?
A) Dénes Kőnig
B) Arthur Cayley
C) Frank Harary
D) Heinrich Heesch
  • 16. Which mathematician's work on trees linked graph theory with theoretical chemistry?
A) Dénes Kőnig
B) Leonhard Euler
C) Frank Harary
D) Arthur Cayley
  • 17. Who published Kirchhoff's circuit laws in 1845?
A) Gustav Kirchhoff
B) Dénes Kőnig
C) Arthur Cayley
D) Leonhard Euler
  • 18. What is the name of the method published by Heinrich Heesch in 1969 for solving the four-color problem?
A) Configuration checking
B) Coloring algorithm
C) Graph reduction
D) Discharging method
  • 19. Who was influential in the field of graph drawing using linear algebraic methods?
A) Dijkstra.
B) Floyd.
C) Euler.
D) W. T. Tutte.
  • 20. Who is credited with the foundational theorem in extremal graph theory?
A) Erdős
B) Mantel
C) Rényi
D) Szemerédi
  • 21. Which data structure lists the neighbors of each vertex separately?
A) Adjacency matrix
B) Adjacency list
C) Edge list
D) Incidence matrix
  • 22. Which decomposition involves covering each edge exactly twice with cycles?
A) Arboricity
B) Graph factorization
C) Cycle double cover
D) Edge coloring
  • 23. What can graph structures represent in evolutionary biology?
A) Evolutionary trees
B) Habitat destruction
C) Species extinction events
D) Genetic mutations
  • 24. What is an Erdős–Rényi model?
A) A technique for partitioning graphs.
B) A model for generating random graphs.
C) An algorithm for graph coloring.
D) A method for finding spanning trees.
  • 25. What is represented by edges in the context of chemical graph theory?
A) Chemical reactions
B) Atoms
C) Bonds
D) Molecules
  • 26. What is the crossing number for a planar graph?
A) Dependent on the weights assigned to edges.
B) One.
C) Zero.
D) Equal to the number of vertices.
  • 27. Who wrote the first textbook on graph theory, published in 1936?
A) Arthur Cayley
B) Leonhard Euler
C) Dénes Kőnig
D) Frank Harary
  • 28. What is a common method in phonology that uses lattice graphs?
A) Graph databases
B) Semantic networks
C) Optimality theory
D) Head-driven phrase structure grammar
  • 29. Which theorem states that every finite group is the group of symmetries of a finite undirected graph?
A) Euler's theorem
B) Paley's theorem
C) Sylow's theorem
D) Frucht's theorem
  • 30. Who generalized the results of Pólya between 1935 and 1937?
A) Nicolaas Govert de Bruijn
B) Heinrich Heesch
C) Arthur Cayley
D) Frank Harary
  • 31. In the context of porous media, what do edges represent?
A) Pores themselves
B) Solid structures
C) Smaller channels connecting the pores
D) Fluid flow paths
  • 32. What is the decomposition of a graph into as few forests as possible called?
A) Graph factorization
B) Cycle double cover
C) Edge coloring
D) Arboricity
  • 33. What is the name of the problem that involves coloring graphs embedded on surfaces with arbitrary genus?
A) Knight's tour problem
B) Graph connectivity problem
C) Graph factorization problem
D) Generalized four-color problem
  • 34. Which type of graph is used in finite-state morphology?
A) Tree-based structures
B) Finite-state transducers
C) Lattice graphs
D) Directed graphs
  • 35. What is the term for a graph where attributes are associated with vertices and edges, often used to model real-world systems?
A) Causal structure
B) Network
C) Semantic network
D) Graph database
  • 36. Which data structure is often preferred for sparse graphs due to smaller memory requirements?
A) List structures
B) Adjacency matrix
C) Incidence matrix
D) Matrix structures
  • 37. What do vertices represent in graphs modeling porous media?
A) Solids
B) Fluids
C) Channels
D) Pores
  • 38. Which problem involves finding a tree connecting a given set of vertices with minimum total edge weight?
A) Hamiltonian path problem
B) Minimum spanning tree
C) Steiner tree
D) Traveling salesman problem
  • 39. In chemistry, what do vertices represent in a molecular graph?
A) Chemical reactions
B) Bonds
C) Molecules
D) Atoms
  • 40. Which problem involves finding a spanning tree with the minimum total edge weight?
A) Steiner tree
B) Traveling salesman problem
C) Minimum spanning tree
D) Hamiltonian path problem
  • 41. Which organization reflects the usefulness of graph theory to linguistics?
A) TextGraphs
B) VerbNet
C) WordNet
D) Finite-state transducers
  • 42. In which field are graphs used to model networks of communication and data organization?
A) Linguistics
B) Computer science
C) Biology
D) Physics
  • 43. In computational linguistics, what type of network is important for modeling word meaning in terms of related words?
A) Graph databases
B) Semantic networks
C) Lattice graphs
D) Syntactic trees
  • 44. What is the principle that gives tree-based structures in linguistics their expressive power?
A) Optimality theory
B) Finite-state transducers
C) Compositionality
D) Feature structures
  • 45. Which branch of algebra focuses on adjacency matrix and its spectrum in spectral graph theory?
A) Number theory
B) Linear algebra
C) Group theory
D) Combinatorics
  • 46. Which matrix is a diagonal matrix representing the degree of a vertex?
A) Degree matrix
B) Incidence matrix
C) Laplacian matrix
D) Adjacency matrix
  • 47. Who asked for a factory plan minimizing crossings between tracks?
A) Karl Menger.
B) Paul Erdős.
C) László Lovász.
D) Hungarian mathematician Pál Turán.
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