  Context. Certain periodic variations of radial velocities (RV) of wobbling
giants originate from exoplanets. Indeed, a number of exoplanets have been
discovered around giant stars.
  Aims. The purpose of our study is to find low-amplitude and long-period RV
variations around bright M (super) giants in the RGB (or AGB) stage, which are
long-period variables (LPVs) or high-proper-motion (HPM) stars.
  Methods. High-resolution, fiber-fed Bohyunsan Observatory Echelle
Spectrograph (BOES) at the Bohyunsan Optical Astronomy Observatory (BOAO) was
used to record numerous spectra of nine giants. The observation period for the
targets spans 16 years, from 2005 to 2022.
  Results. We found from the precise RV observations of nine M giants two
sub-stellar companions, one with a 28.26$^{+2.05}_{-2.17}$ $M_{J}$ orbiting
period of 663.87$^{+4.61}_{-4.31}$ days at a distance of 2.03$^{+0.01}_{-0.01}$
AU (HD 6860) and the other, with a 15.83$^{+2.33}_{-2.74}$ $M_{J}$ orbiting
period of 466.63 $^{+1.47}_{-1.28}$ days at a distance of 1.33
$^{+0.08}_{-0.11}$ AU (HD 112300). Our estimate of the stellar parameters for
HD 6860 makes it currently the largest star with a sub-stellar companion. We
also found RV variations mimicking a planetary companion in HD 18884 and
confirmed LPVs in two stars, HD 39801 and HD 42995. The RV variations of some
stars seem to be associated with stellar activities rather than reflex orbital
motion due to their companions. Such variations are also detected even for HD
6860 and HD 112300, hosting sub-stellar companions.
