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 line graph
B) A chart or diagram
C) A pie chart
D) A mathematical structure consisting of vertices and edges
  • 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 loop on a vertex
B) A node's color in a graph
C) A vertex with no connections
D) A connection between two vertices
  • 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 disconnected graph
D) A cycle in a graph
  • 5. In a simple graph, can an edge connect a vertex to itself?
A) Depends on the number of vertices
B) Sometimes
C) No
D) Yes
  • 6. What is the degree of a vertex in a graph?
A) The number of vertices in the graph
B) The distance from one vertex to another
C) The size of the graph
D) The number of edges incident to the vertex
  • 7. What is a planar graph?
A) A disconnected graph
B) A graph that can be drawn on a plane without any edge intersections
C) A graph with cycles
D) A multigraph
  • 8. What is a weighted graph?
A) A graph with maximum number of edges
B) A graph in which a number (weight) is assigned to each edge
C) An undirected graph
D) A graph with only one vertex
  • 9. What is an isomorphism between two graphs?
A) A bijection between their vertex sets that preserves edges
B) Two disconnected graphs
C) The same number of vertices in both graphs
D) A loop on a vertex in both graphs
  • 10. What was the title of Leonhard Euler's paper that is considered the first in graph theory?
A) Graph Theory and its Applications
B) Solutio Problematis ad Geometriam Situs Pertinentis
C) The Seven Bridges of Königsberg
D) On the Nature of Graphs
  • 11. What type of graph allows edges to connect a vertex to itself?
A) Directed graph
B) Multigraph
C) Undirected graph
D) Simple graph
  • 12. Who introduced the term 'graph' in the context of mathematics?
A) Leonhard Euler
B) Dénes Kőnig
C) Arthur Cayley
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) Knight's tour problem
B) Graph connectivity problem
C) Seven Bridges problem
D) Four-color 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) Frank Harary
B) Arthur Cayley
C) Dénes Kőnig
D) Heinrich Heesch
  • 16. Which mathematician's work on trees linked graph theory with theoretical chemistry?
A) Leonhard Euler
B) Dénes Kőnig
C) Frank Harary
D) Arthur Cayley
  • 17. Who published Kirchhoff's circuit laws in 1845?
A) Dénes Kőnig
B) Gustav Kirchhoff
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) Graph reduction
B) Coloring algorithm
C) Discharging method
D) Configuration checking
  • 19. Who was influential in the field of graph drawing using linear algebraic methods?
A) Floyd.
B) Dijkstra.
C) W. T. Tutte.
D) Euler.
  • 20. Who is credited with the foundational theorem in extremal graph theory?
A) Mantel
B) Rényi
C) Szemerédi
D) Erdős
  • 21. Which data structure lists the neighbors of each vertex separately?
A) Adjacency matrix
B) Incidence matrix
C) Adjacency list
D) Edge list
  • 22. Which decomposition involves covering each edge exactly twice with cycles?
A) Cycle double cover
B) Graph factorization
C) Arboricity
D) Edge coloring
  • 23. What can graph structures represent in evolutionary biology?
A) Genetic mutations
B) Evolutionary trees
C) Species extinction events
D) Habitat destruction
  • 24. What is an Erdős–Rényi model?
A) An algorithm for graph coloring.
B) A model for generating random graphs.
C) A method for finding spanning trees.
D) A technique for partitioning graphs.
  • 25. What is represented by edges in the context of chemical graph theory?
A) Molecules
B) Chemical reactions
C) Atoms
D) Bonds
  • 26. What is the crossing number for a planar graph?
A) Equal to the number of vertices.
B) One.
C) Zero.
D) Dependent on the weights assigned to edges.
  • 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) Semantic networks
B) Optimality theory
C) Graph databases
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) Sylow's theorem
B) Frucht's theorem
C) Paley's theorem
D) Euler's theorem
  • 30. Who generalized the results of Pólya between 1935 and 1937?
A) Arthur Cayley
B) Nicolaas Govert de Bruijn
C) Frank Harary
D) Heinrich Heesch
  • 31. In the context of porous media, what do edges represent?
A) Fluid flow paths
B) Solid structures
C) Smaller channels connecting the pores
D) Pores themselves
  • 32. What is the decomposition of a graph into as few forests as possible called?
A) Arboricity
B) Graph factorization
C) Edge coloring
D) Cycle double cover
  • 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) Generalized four-color problem
D) Graph factorization problem
  • 34. Which type of graph is used in finite-state morphology?
A) Tree-based structures
B) Directed graphs
C) Finite-state transducers
D) Lattice 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) Semantic network
B) Causal structure
C) Network
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) Channels
B) Pores
C) Solids
D) Fluids
  • 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) Chemical reactions
B) Atoms
C) Molecules
D) Bonds
  • 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) Finite-state transducers
B) TextGraphs
C) WordNet
D) VerbNet
  • 42. In which field are graphs used to model networks of communication and data organization?
A) Physics
B) Computer science
C) Biology
D) Linguistics
  • 43. In computational linguistics, what type of network is important for modeling word meaning in terms of related words?
A) Syntactic trees
B) Graph databases
C) Lattice graphs
D) Semantic networks
  • 44. What is the principle that gives tree-based structures in linguistics their expressive power?
A) Finite-state transducers
B) Compositionality
C) Feature structures
D) Optimality theory
  • 45. Which branch of algebra focuses on adjacency matrix and its spectrum in spectral graph theory?
A) Combinatorics
B) Group theory
C) Linear algebra
D) Number theory
  • 46. Which matrix is a diagonal matrix representing the degree of a vertex?
A) Adjacency matrix
B) Incidence matrix
C) Laplacian matrix
D) Degree matrix
  • 47. Who asked for a factory plan minimizing crossings between tracks?
A) Karl Menger.
B) László Lovász.
C) Paul Erdős.
D) Hungarian mathematician Pál Turán.
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