Zero-symmetric graph

[1] The name for this class of graphs was coined by R. M. Foster in a 1966 letter to H. S. M.

However, there exist larger examples of zero-symmetric graphs that are not bipartite.

The smallest such graph has 20 vertices, with LCF notation [6,6,-6,-6]5.

[8] All known finite connected zero-symmetric graphs contain a Hamiltonian cycle, but it is unknown whether every finite connected zero-symmetric graph is necessarily Hamiltonian.

[9] This is a special case of the Lovász conjecture that (with five known exceptions, none of which is zero-symmetric) every finite connected vertex-transitive graph and every finite Cayley graph is Hamiltonian.