Graph theory Please provide whole solution for the question

Graph theory.

Please provide whole solution for the question with any examples such as picture or graph.

Q) FInd an application for Hamilton path or Hamilton closed path.

Solution

In general, the problem of finding a Hamiltonian path is NP-complete (Garey and Johnson 1983, pp. 199-200), so the only known way to determine whether a given general graph has a Hamiltonian path is to undertake an exhaustive search

Any bipartite graph with a vertex parity unbalance >1 has no Hamiltonian paths.