A systematic study of the isoscalar giant monopole resonance (ISGMR) in a wide range of nuclei from various isotopic chains is performed within the microscopic self-consistent Skyrme Hartree-Fock plus Bardeen-Cooper-Schrieffer ($\mathrm{HF}+\mathrm{BCS}$) method and coherent density fluctuation model (CDFM). The calculations for the nuclear incompressibility are based on the Brueckner and Barcelona-Catania-Paris-Madrid (BCPM) energy density functionals for nuclear matter using the capability of the CDFM to make a transition to the corresponding incompressibility in finite nuclei. The results obtained by applying different definitions of the ISGMR energy, as well as the two energy-density functionals, are analyzed and compared with the available experimental data. The peculiarities of the proton and neutron density distributions and their corresponding linear size characteristics are considered. In general, a connection with the measured neutron skin thicknesses is proposed as a possible way to obtain realistic estimations of the energy of ISGMR.

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• Giant resonances
• Nuclear density functional theory
• Nuclear matter
• Nuclear radii