The charm (D) and charm-strange ( \(D_s\) ) mesons are investigated in a variational scheme using Gaussian trial wave functions. The Hamiltonian contains Song and Lin potential with a constant term dependent on radial and orbital quantum numbers. The Gaussian wave function used has a dependence on radial distance r, radial quantum number n, orbital quantum number l and a trial parameter \(\mu \) . The obtained spectra of D and \(D_s\) mesons are in good agreement with other theoretical models and available experimental masses. The mass spectra of D and \(D_s\) mesons are also used to plot Regge trajectories in the (J, \(M^2\) ) and ( \(n_r\) , \(M^2\) ) planes. In (J, \(M^2\) ) plane, both natural and unnatural parity states of D and \(D_s\) mesons are plotted. The trajectories are parallel and equidistant from each other. The two-body strong decays of D and \(D_s\) are analyzed in the framework of heavy quark effective theory using computed masses. The strong decay widths are given in terms of strong coupling constants. These couplings are also estimated by comparing them with available experimental values for observed states. Also, the partial decay width ratios of different states are analyzed and used to suggest assignments to the observed states. We have assigned the spin-parity to newly observed \(D^*_{s2}(2573)\) as the strange partner of \(D^*_2(2460)\) identified as \(1^3P_2\) , \(D_1^*(2760)\) and \(D^*_{s1}(2860)\) as \(1^3D_1\) , \(D^*_3(2750)\) and \(D^*_{s3}(2860)\) as \(1^3D_3\) , \(D_2(2740)\) as \(1D_2\) , \(D_0(2550)\) as \(2^1S_0\) , \(D^*_1(2660)\) and \(D^*_{s1}(2700)\) as \(2^3S_1\) , \(D^*_J(3000)\) as \(2^3P_0\) , \(D_J(3000)\) as \(2P_1\) , \(D^*_2(3000)\) as \(1^3F_2\) states.
