  A correlation between the charge radii difference of mirror partner nuclei
$\Delta{R_{\mathrm{ch}}}$ and the slope parameter $L$ of symmetry energy has
been built to ascertain the equation of state of isospin asymmetric nuclear
matter. In this work, the influences of pairing correlations and isoscalar
compression modulus on the \Delta{R_{\mathrm{ch}}}$ are systematically
investigated based on the Skyrme energy density functional theory. The
calculated results suggest that the linear correlation between
$\Delta{R_{\mathrm{ch}}}$ and $L$ is decreased by the surface pairing
correlations. The slope parameter deduced from the difference of charge radii
of mirror-pair nuclei $^{32}$Ar-$^{32}$Si, $^{36}$Ca-$^{36}$S,
$^{38}$Ca-$^{38}$Ar, and $^{54}$Ni-$^{54}$Fe falls into the range of
$L=42.57$-$50.64$ MeV, that is, the rather soft equation of state of asymmetric
nuclear matter. Besides, the range of the slope parameter can also be
influenced by the effective forces classified by various isoscalar
incompressibility coefficients.
