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This paper theoretically investigates the propagation of Lamb waves in a two-dimensional (2D) phononic crystal (PC) structure composed of multiple square stubs symmetric or anti-symmetric deposited on a thin homogeneous plate. The dispersion relations, the power transmission spectra and the displacement fields of the eigenmodes are studied by using the finite-element method (FEM). We investigate the effect of the distance between adjacent square stubs on the band gaps (BGs). The results show that the distance between adjacent square stubs can remarkably change the location and the width of the BGs. Meanwhile, we conducted a numerically study on the different results between the anti-symmetric and symmetric distribution of the scatterers. The band structure of the anti-symmetric structure PC is significantly different from the symmetric structure. In general, the distribution of the square stubs has an influence on the band structures. We further identify the physical mechanism of the distinction in the formation of the BG between the anti-symmetric and the symmetric model through the displacement fields of the eigenmodes. In addition, we find that the variation of the PC BGs in anti-symmetric and symmetric structure are sensitive to the distance between adjacent square stubs, which could be indispensable to practical applications such as BG tuning. [ABSTRACT FROM AUTHOR]