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Hyper-Hamiltonicity analysis of generalized Petersen graphs P(n,2)

This paper studies the classification of the Hamiltonicity of generalized Petersen graphs P(n,2) with even n by using the self-organizing algorithm (SOA). The main work of this paper is theoretical proof of the classification conditions set up. Meanwhile, some new, more detailed classification conditions are set up in this paper as new conjectures were found by analyzing the results of the study and some theorems about inner and outer Half-Hyper-Hamiltonian graphs are proven, laying the basis for making further theoretical studies in this field.