Graph Theory Quiz

Quiz 8 Discrete Mathematics II

• A graph G is given, and the task is to:
  • Number the vertices from 1 to 7 and determine the degree of each vertex
  • Determine the number of automorphisms the graph has

Quiz 7 Discrete Mathematics II

• Two graphs G and H are given, and the task is to:
  • Determine the order (number of vertices) of each graph
  • Determine the size (number of edges) of each graph
  • Determine the degree sequence (the sequence of vertex degrees) of each graph
  • Determine if the two graphs are isomorphic
    • If they are, provide an explicit isomorphism ( vertex labeling and mapping)
    • If they are not, provide a reason to prove they are not

Quiz 6 Discrete Mathematics II

• The task is to:
  • Explain why there can be no simple graph with degree sequence (2, 2, 6, 6, 6, 6, 6)
  • Consider a graph G with size 20, and:
    • 2 vertices of degree 5
    • 3 vertices of degree 4
    • Remaining vertices have degree 3
  • Determine the possible orders of G and sketch one possible graph for each possibility

This quiz covers topics in Discrete Mathematics II, focusing on graph theory. It includes questions related to vertex numbering, degrees, automorphisms, graph order, size, and degree sequences. Test your knowledge in these areas and enhance your understanding of graph theory concepts.