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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 line graph
B) A pie chart
C) A mathematical structure consisting of vertices and edges
D) A chart or diagram
  • 2. What is a vertex in a graph?
A) A line connecting two points in a graph
B) A function in graph theory
C) A path between two vertices
D) A point or node in a graph
  • 3. What is an edge in a graph?
A) A loop on a vertex
B) A connection between two vertices
C) A node's color in a graph
D) A vertex with no connections
  • 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) Sometimes
B) Yes
C) Depends on the number of vertices
D) No
  • 6. What is the degree of a vertex in a graph?
A) The distance from one vertex to another
B) The number of vertices in the graph
C) The number of edges incident to the vertex
D) The size of the graph
  • 7. What is a planar graph?
A) A disconnected graph
B) A graph with cycles
C) A graph that can be drawn on a plane without any edge intersections
D) A multigraph
  • 8. What is a weighted graph?
A) A graph in which a number (weight) is assigned to each edge
B) An undirected graph
C) A graph with only one vertex
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) Two disconnected graphs
C) A bijection between their vertex sets that preserves edges
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) The Seven Bridges of Königsberg
B) Graph Theory and its Applications
C) Solutio Problematis ad Geometriam Situs Pertinentis
D) On the Nature of Graphs
  • 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) Dénes Kőnig
C) James Joseph Sylvester
D) Arthur Cayley
  • 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) Four-color problem
B) Seven Bridges problem
C) Graph connectivity problem
D) Knight's tour problem
  • 14. Who first posed the four-color problem?
A) Augustus De Morgan
B) William Rowan Hamilton
C) Peter Tait
D) Francis Guthrie
  • 15. Who donated all royalties from their textbook on graph theory to fund the Pólya Prize?
A) Arthur Cayley
B) Dénes Kőnig
C) Frank Harary
D) Heinrich Heesch
  • 16. Which mathematician's work on trees linked graph theory with theoretical chemistry?
A) Frank Harary
B) Dénes Kőnig
C) Leonhard Euler
D) Arthur Cayley
  • 17. Who published Kirchhoff's circuit laws in 1845?
A) Leonhard Euler
B) Arthur Cayley
C) Gustav Kirchhoff
D) Dénes Kőnig
  • 18. What is the name of the method published by Heinrich Heesch in 1969 for solving the four-color problem?
A) Coloring algorithm
B) Graph reduction
C) Configuration checking
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) Mantel
B) Rényi
C) Szemerédi
D) Erdős
  • 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) Edge coloring
B) Graph factorization
C) Cycle double cover
D) Arboricity
  • 23. What can graph structures represent in evolutionary biology?
A) Habitat destruction
B) Evolutionary trees
C) Species extinction events
D) Genetic mutations
  • 24. What is an Erdős–Rényi model?
A) An algorithm for graph coloring.
B) A technique for partitioning graphs.
C) A method for finding spanning trees.
D) A model for generating random graphs.
  • 25. What is represented by edges in the context of chemical graph theory?
A) Molecules
B) Bonds
C) Atoms
D) Chemical reactions
  • 26. What is the crossing number for a planar graph?
A) Equal to the number of vertices.
B) One.
C) Dependent on the weights assigned to edges.
D) Zero.
  • 27. Who wrote the first textbook on graph theory, published in 1936?
A) Arthur Cayley
B) Frank Harary
C) Leonhard Euler
D) Dénes Kőnig
  • 28. What is a common method in phonology that uses lattice graphs?
A) Graph databases
B) Head-driven phrase structure grammar
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) Sylow's theorem
C) Paley's theorem
D) Frucht'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) Smaller channels connecting the pores
B) Pores themselves
C) Solid structures
D) Fluid flow paths
  • 32. What is the decomposition of a graph into as few forests as possible called?
A) Graph factorization
B) Edge coloring
C) Arboricity
D) Cycle double cover
  • 33. What is the name of the problem that involves coloring graphs embedded on surfaces with arbitrary genus?
A) Graph factorization problem
B) Generalized four-color problem
C) Knight's tour problem
D) Graph connectivity problem
  • 34. Which type of graph is used in finite-state morphology?
A) Finite-state transducers
B) Lattice graphs
C) Tree-based structures
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) Network
B) Semantic network
C) Graph database
D) Causal structure
  • 36. Which data structure is often preferred for sparse graphs due to smaller memory requirements?
A) Adjacency matrix
B) Matrix structures
C) Incidence matrix
D) List structures
  • 37. What do vertices represent in graphs modeling porous media?
A) Fluids
B) Pores
C) Solids
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) Hamiltonian path problem
C) Traveling salesman problem
D) Steiner tree
  • 39. In chemistry, what do vertices represent in a molecular graph?
A) Chemical reactions
B) Atoms
C) Bonds
D) Molecules
  • 40. Which problem involves finding a spanning tree with the minimum total edge weight?
A) Steiner tree
B) Hamiltonian path problem
C) Traveling salesman problem
D) Minimum spanning tree
  • 41. Which organization reflects the usefulness of graph theory to linguistics?
A) VerbNet
B) WordNet
C) Finite-state transducers
D) TextGraphs
  • 42. In which field are graphs used to model networks of communication and data organization?
A) Biology
B) Computer science
C) Linguistics
D) Physics
  • 43. In computational linguistics, what type of network is important for modeling word meaning in terms of related words?
A) Lattice graphs
B) Graph databases
C) Syntactic trees
D) Semantic networks
  • 44. What is the principle that gives tree-based structures in linguistics their expressive power?
A) Compositionality
B) Feature structures
C) Optimality theory
D) Finite-state transducers
  • 45. Which branch of algebra focuses on adjacency matrix and its spectrum in spectral graph theory?
A) Combinatorics
B) Linear algebra
C) Number theory
D) Group theory
  • 46. Which matrix is a diagonal matrix representing the degree of a vertex?
A) Incidence matrix
B) Degree matrix
C) Laplacian 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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