On Sheehan's Conjecture for Graphs with Symmetry
Sheehan's Conjecture states that every hamiltonian 4-regular graph possesses a second Hamilton cycle. In this article, we verify Sheehan's Conjecture for 4-regular graphs of order n whose automorphism group has size at least if either for all , or for and m is either an odd prime or a power of 2. We also give lower bounds on the size of the automorphism group and degree of a regular hamiltonian graph that guarantee existence of a second Hamilton cycle.
sheehan's conjecture hamilton cycle automorphism group regular graph