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