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Hamilton-Connected Harary Graphs

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size of Harary graph
33
path start
3
path end
19
hide vertex labels
hide path
The Harary graphs
H
k,n
are a specifically defined family of graphs on
n
vertices that are
k
-connected and have the minimum possible number of edges for such a graph,
⌈1/2kn⌉
. A path is Hamiltonian if it visits all vertices without repetition. This Demonstration illustrates a proof that
H
3,n
, where
n
has the form
4r+1
, admits a Hamiltonian path from any vertex to any other. (The start vertex is green and end vertex is red.)
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