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We investigate magnetic activity properties of 21 stars via medium resolution optical spectra and long-term photometry. Applying synthetic spectrum fitting method, we find that all targets are cool giant or sub-giant stars possessing overall [M/H] abundances between 0 and -0.5. We find that six of these targets exhibit only linear trend in mean brightness, while eight of them clearly shows cyclic mean brightness variation. Remaining seven target appear to exhibit cyclicmean brightness variation, but this cannot be confirmed due to the long timescales of the predicted cycle compared to the current time range of the photometric data. We further determine seasonal photometric periods and compute average photometric period of each target. Analysed sample in this study provides a quantitative representation of a positive linear correlation between the inverse of the rotation period and the cycle period normalised to the rotation period, on the log-log scale. We also observe no correlation between the activity cycle length and the relative surface shear, indicating that the activity cycle must be driven by a parameter rather than the differential rotation. Our analyses show that the relative surface shear is positively correlated with the rotation period and there is a noticeable separation between main sequence stars and our sample. Compared to our sample, the relative surface shear of a main sequence star is larger for a given rotation period. However, dependence of the relative surface shear on the rotation period appears stronger for our sample. Analysis of the current photometric data indicates that the photometric properties of the observed activity cycles in eight targets seem dissimilar to the sunspot cycle.Y, TuBTAK National Observatory [14BRTT150-678, 18BRTT150-1275], I am indebted to Dr. Grzegorz Pojmaski for reducing and providing unpublished ASAS-3N data, which compensate long data gap between published ASAS3 and ASAS-SN data and increase the precision of the main results of this study. I also express my thanks to Dr. Hasan Ali Dal for fruitful discussion on statistical analyses. I acknowledge the anonymous referee for his/her helpful comments and valuable suggestions that have significantly contributed to improve the paper. I further thank TuBTAK National Observatory for a partial support in using RTT150 (Russian-Turkish 1.5-m telescope in Antalya) with project numbers 14BRTT150-678 and 18BRTT150-1275. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France. This research received no specific grant from any funding agency, commercial, or not-for-profit sectors.

Studying RS CVn binaries is challenging, because in addition to spot activity, other effects such as mass transfer between the components and gravitational distortion of their spherical forms may distort their light curves. Such effects can, however, be removed from the data by subtracting a mean light curve phased with the orbital period. We study a quarter of a century of standard Johnson differential V photometry of the RS CVn binary BM CVn. Our main aims are to determine the activity cycles, the rate of surface differential rotation and the rotation period of the active longitudes of BM CVn. The Continuous Period Search (CPS) is applied to the photometry. The changes of the mean and amplitude of the light curves are used to search for activity cycles. The rotation period changes give an estimate of the rate of surface differential rotation. The Kuiper method is applied to the epochs of the primary and secondary minima to search for active longitudes. The photometry reveals the presence of a stable mean light curve (MLC) connected to the orbital period P_orb = 20d.6252 of this binary. We remove this MLC from the original V magnitudes which gives us the corrected V' magnitudes. These two samples of V and V' data are analysed separately with CPS. The fraction of unreliable CPS models decreases when the MLC is removed. The same significant activity cycle of approximately 12.5 years is detected in both V and V' samples. The estimate for the surface differential rotation coefficient, k >= 0.10, is the same for both samples, but the number of unrealistic period estimates decreases after removing the MLC. The same active longitude period of P_al = 20d.511 +- 0d.005 is detected in the V and V' magnitudes. This long-term regularity in the epochs of primary and secondary minima of the light curves is not caused by the MLC. On the contrary, the MLC hampers the detection of active longitudes., 11 pages, 13 figures