  Asteroseismology offers a profound window into stellar interiors and has
emerged as a pivotal technique in exoplanetary research. This study harnesses
the Transiting Exoplanet Survey Satellite (TESS) observations to reveal, for
the first time, the asteroseismic oscillations of four exoplanet-hosting stars.
Through meticulous analysis, we extracted their asteroseismic signatures,
enabling the precise determination of stellar masses, radii, luminosities, and
surface gravities. These parameters exhibit markedly reduced uncertainties
compared to those derived from spectroscopic methods. Crucially, the exoplanets
orbiting these stars were initially identified via radial velocity
measurements. The refinement of host stellar masses necessitates a
corresponding adjustment in planetary characteristics. Employing
asteroseismology, we recalibrated the exoplanets' minimum masses and semi-major
axes - a novel approach in the field. For instance, the exoplanet HD 5608 b's
minimum mass, denoted as Msini, was ascertained to be 1.421 +/- 0.091 M_J
through the integration of asteroseismic and radial velocity data. Similarly,
two planets within the 7 CMa system yielded Msini values of 1.940 +/- 0.064 MJ
and 0.912 +/- 0.067 M_J, respectively. Two planets in HD 33844 system presented
Msini figures of 1.726 +/- 0.145 M_J and 1.541 +/- 0.182 M_J, while the HIP
67851 system's planets registered Msini at 1.243 +/- 0.139 M_J and a notably
higher 5.387 +/- 0.699 M_J. This investigation extends beyond mere parameter
refinement; it underscores the synergy between asteroseismology and
exoplanetology, yielding unprecedented precision in system metrics. Focusing on
quartet of K-type giants in advanced evolutionary phases, our work positions
these systems as invaluable astrophysical laboratories, offering insights into
the potential trajectory of our own solar system's fate.
