  Context: Molecular clouds are the prime locations of star formation. These
clouds contain filamentary structures and cores which are crucial in the
formation of young stars. Aims: In this work, we aim to quantify the physical
properties of structural characteristics within the molecular cloud L1251 to
better understand the initial conditions for star formation. Methods: We
applied the getsf algorithm to identify cores and filaments within the
molecular cloud L1251 using the Herschel multiband dust continuum image,
enabling us to measure their respective physical properties. Additionally, we
utilized an enhanced differential term algorithm to produce high-resolution
temperature maps and column density maps with a resolution of ${13.5}''$.
Results: We identified 122 cores in the region. Out of them, 23 are
protostellar cores, 13 are robust prestellar cores, 32 are candidate prestellar
cores (including 13 robust prestellar cores and 19 strictly candidate
prestellar cores), and 67 are unbound starless cores. getsf also found 147
filament structures in the region. Statistical analysis of the physical
properties (mass (M), temperature (T), size, and core brightness (hereafter, we
are using the word luminosity (L)) for the core brightness) of obtained cores
shows a negative correlation between core mass and temperature and a positive
correlation between (M/L) and (M/T). Analysis of the filaments gives a median
width of 0.14 pc and no correlation between width and length. Out of those 122
cores, 92 are present in filaments (75.4%) and the remaining were outside them.
Out of the cores present in filaments, 57 (62%) cores are present in
supercritical filaments ($M_{\rm line}>16M_{\odot }/{\rm pc}$).
