Relationship Between Major Stellar Physical Parameters and Normal Mode Frequencies in Accreting White Dwarf Stars

White dwarfs (WDs) are the final fate of about 97% of the stars in our galaxy, making them vital tracers of stellar history. A fraction of WDs exist in cataclysmic variable (CV) systems, accreting matter from a nearby companion star. A subset of CVs undergo episodic rapid mass transfer, termed dwarf novae (DNe) outbursts. Some accreting WDs exhibit near sinusoidal photometric variations, interpreted as $g$ mode pulsations. However, identifying pulsation modes in accreting WDs remains challenging due to the paucity of available observed modes. In this work, we present a comprehensive computation of the observable $g$ mode frequencies across a range of WD parameters, varying the WD mass, size of the newly accreted layer and core temperature. We also introduce a novel method for mode identification based on the time evolution of pulsation periods following an accretion episode. Our mode identification method does not rely on the direct detection of the consecutive radial mode orders, frequently required in isolated WDs. Moreover, this work improves upon our previous WD modeling efforts. We use a more realistic core temperature in addition to thermohaline mixing and element diffusion enabled during the accretion phase.