Context : Ultra-massive hydrogen-rich white dwarf stars are expected to harbor oxygen/neon cores resulting from the progenitor evolution through the super-asymptotic giant branch phase .
As evolution proceeds during the white dwarf cooling phase , a crystallization process resulting from Coulomb interactions in very dense plasmas is expected to occur , leading to the formation of a highly crystallized core .
In particular , pulsating ultra-massive white dwarfs offer a unique opportunity to infer and test the occurrence of crystallization in white dwarf interiors as well as physical processes related with dense plasmas .

Aims : We aim to assess the adiabatic pulsation properties of ultra-massive hydrogen-rich white dwarfs with oxygen/neon cores .

Methods : We studied the pulsation properties of ultra-massive hydrogen-rich white dwarf stars with oxygen/neon cores .
We employed a new set of ultra-massive white dwarf evolutionary sequences of models with stellar masses in the range 1.10 \leq M _ { \star } / M _ { \sun } \leq 1.29 computed by taking into account the complete evolution of the progenitor stars and the white dwarf stage .
During the white dwarf cooling phase , we considered element diffusion .
When crystallization set on in our models , we took into account latent heat release and also the expected changes in the core chemical composition that are due to phase separation according to a phase diagram suitable for oxygen and neon plasmas .
We computed nonradial pulsation g -modes of our sequences of models at the ZZ Ceti phase by taking into account a solid core .
We explored the impact of crystallization on their pulsation properties , in particular , the structure of the period spectrum and the distribution of the period spacings .

Results : We find that it would be possible , in principle , to discern whether a white dwarf has a nucleus made of carbon and oxygen or a nucleus of oxygen and neon by studying the spacing between periods .

Conclusions : The features found in the period-spacing diagrams could be used as a seismological tool to discern the core composition of ultra-massive ZZ Ceti stars , something that should be complemented with detailed asteroseismic analysis using the individual observed periods .