ThatQuiz Test Library Take this test now
Graph theory - Exam
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 pie chart
B) A mathematical structure consisting of vertices and edges
C) A line graph
D) A chart or diagram
  • 2. What is a vertex in a graph?
A) A line connecting two points in a graph
B) A path between two vertices
C) A function in graph theory
D) A point or node in a graph
  • 3. What is an edge in a graph?
A) A connection between two vertices
B) A node's color in a graph
C) A vertex with no connections
D) A loop on a vertex
  • 4. What is a path in graph theory?
A) A cycle in a graph
B) A disconnected graph
C) A sequence of edges that connect a sequence of vertices
D) An isolated vertex
  • 5. In a simple graph, can an edge connect a vertex to itself?
A) Depends on the number of vertices
B) Sometimes
C) Yes
D) No
  • 6. What is the degree of a vertex in a graph?
A) The number of vertices in the graph
B) The size of the graph
C) The number of edges incident to the vertex
D) The distance from one vertex to another
  • 7. What is a planar graph?
A) A graph that can be drawn on a plane without any edge intersections
B) A multigraph
C) A disconnected graph
D) A graph with cycles
  • 8. What is a weighted graph?
A) A graph with maximum number of edges
B) An undirected graph
C) A graph with only one vertex
D) A graph in which a number (weight) is assigned to each edge
  • 9. What is an isomorphism between two graphs?
A) A bijection between their vertex sets that preserves edges
B) The same number of vertices in both graphs
C) A loop on a vertex in both graphs
D) Two disconnected 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) Solutio Problematis ad Geometriam Situs Pertinentis
C) Graph Theory and its Applications
D) On the Nature of Graphs
  • 11. What type of graph allows edges to connect a vertex to itself?
A) Multigraph
B) Undirected graph
C) Simple graph
D) Directed 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) Seven Bridges problem
B) Graph connectivity problem
C) Knight's tour problem
D) Four-color problem
  • 14. Who first posed the four-color problem?
A) William Rowan Hamilton
B) Augustus De Morgan
C) Peter Tait
D) Francis Guthrie
  • 15. Who donated all royalties from their textbook on graph theory to fund the Pólya Prize?
A) Heinrich Heesch
B) Dénes Kőnig
C) Arthur Cayley
D) Frank Harary
  • 16. Which mathematician's work on trees linked graph theory with theoretical chemistry?
A) Leonhard Euler
B) Arthur Cayley
C) Dénes Kőnig
D) Frank Harary
  • 17. Who published Kirchhoff's circuit laws in 1845?
A) Dénes Kőnig
B) Gustav Kirchhoff
C) Leonhard Euler
D) Arthur Cayley
  • 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) W. T. Tutte.
B) Dijkstra.
C) Floyd.
D) Euler.
  • 20. Who is credited with the foundational theorem in extremal graph theory?
A) Rényi
B) Erdős
C) Mantel
D) Szemerédi
  • 21. Which data structure lists the neighbors of each vertex separately?
A) Adjacency list
B) Adjacency matrix
C) Incidence matrix
D) Edge list
  • 22. Which decomposition involves covering each edge exactly twice with cycles?
A) Cycle double cover
B) Edge coloring
C) Arboricity
D) Graph factorization
  • 23. What can graph structures represent in evolutionary biology?
A) Species extinction events
B) Habitat destruction
C) Evolutionary trees
D) Genetic mutations
  • 24. What is an Erdős–Rényi model?
A) A technique for partitioning graphs.
B) A method for finding spanning trees.
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) Bonds
C) Chemical reactions
D) Molecules
  • 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) Arthur Cayley
B) Frank Harary
C) Dénes Kőnig
D) Leonhard Euler
  • 28. What is a common method in phonology that uses lattice graphs?
A) Head-driven phrase structure grammar
B) Optimality theory
C) Graph databases
D) Semantic networks
  • 29. Which theorem states that every finite group is the group of symmetries of a finite undirected graph?
A) Paley's theorem
B) Frucht's theorem
C) Sylow's theorem
D) Euler's theorem
  • 30. Who generalized the results of Pólya between 1935 and 1937?
A) Arthur Cayley
B) Heinrich Heesch
C) Nicolaas Govert de Bruijn
D) Frank Harary
  • 31. In the context of porous media, what do edges represent?
A) Fluid flow paths
B) Pores themselves
C) Solid structures
D) Smaller channels connecting the pores
  • 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) Graph connectivity problem
B) Knight's tour problem
C) Graph factorization problem
D) Generalized four-color problem
  • 34. Which type of graph is used in finite-state morphology?
A) Lattice graphs
B) Tree-based structures
C) Finite-state transducers
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) Graph database
B) Network
C) Semantic network
D) Causal structure
  • 36. Which data structure is often preferred for sparse graphs due to smaller memory requirements?
A) List structures
B) Matrix structures
C) Incidence matrix
D) Adjacency matrix
  • 37. What do vertices represent in graphs modeling porous media?
A) Fluids
B) Solids
C) Pores
D) Channels
  • 38. Which problem involves finding a tree connecting a given set of vertices with minimum total edge weight?
A) Hamiltonian path problem
B) Steiner tree
C) Traveling salesman problem
D) Minimum spanning tree
  • 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) Minimum spanning tree
B) Traveling salesman problem
C) Hamiltonian path problem
D) Steiner tree
  • 41. Which organization reflects the usefulness of graph theory to linguistics?
A) VerbNet
B) Finite-state transducers
C) WordNet
D) TextGraphs
  • 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) Feature structures
B) Compositionality
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) Group theory
D) Number theory
  • 46. Which matrix is a diagonal matrix representing the degree of a vertex?
A) Degree matrix
B) Adjacency matrix
C) Incidence matrix
D) Laplacian matrix
  • 47. Who asked for a factory plan minimizing crossings between tracks?
A) Karl Menger.
B) Hungarian mathematician Pál Turán.
C) Paul Erdős.
D) László Lovász.
Created with That Quiz — the site for test creation and grading in math and other subjects.