This project is an intensive study of Eulerian and Hamiltonian graphs. Choose a graph of your own. – For the graph you have come up with, complete the following tasks:
— Label the vertices and provide the vertex set and edge set. — State degree sequence and provide the adjacency matrix. — Find either an Eulerian circuit or an Eulerian trail for the graph. — Determine whether or not the graph is Hamiltonian, and then give the Hamiltonian cycle OR show why the graph is not Hamiltonian. — State the edge-connectivity and connectivity (vertex connectivity) for the graph.
— Give a cutset for the graph that results in no isolated vertices. A few notes about format: use MS PowerPoint for your presentation; develop a presentation that is 10-20 slides in length; incorporate audio files into your presentation in order to explain your work; use Equation Editor for all mathematical symbols, e.g. x ∈ X or Cl(A) ⋂ Cl(X-A); and select fonts, backgrounds, etc. to make your presentation look professional.
