# Hamilton-Connected Harary Graphs

Hamilton-Connected Harary Graphs

The Harary graphs are a specifically defined family of graphs on vertices that are -connected and have the minimum possible number of edges for such a graph, . A path is Hamiltonian if it visits all vertices without repetition. This Demonstration illustrates a proof that , where has the form , admits a Hamiltonian path from any vertex to any other. (The start vertex is green and end vertex is red.)

H

k,n

n

k

⌈1/2kn⌉

H

3,n

n

4r+1