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.

Eulerian and Hamiltonian graphs

This Paper 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  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 20-25 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.