  The $\alpha$-decay half-lives of superheavy nuclei with $100 \leq Z \leq 120$
are comprehensively analyzed using the axially deformed relativistic mean field
(RMF) formalism for the NL3$^*$ parameter set. We employ RMF binding energies
to determine the $\alpha$-decay energies and make a comparison with both the
available experimental data and the theoretical results obtained from the
global nuclear mass model WS4. The four distinct formulae, specifically the
modified scaling law Brown, modified Viola-Seaborg, Yibin {\it et al.} formula,
and its modified form are used to calculate the decay half-lives and examine
the numerical correlation between the half-life ($T_{1/2}$) for each
$\alpha$-decay energy. We notice that $T_{1/2}$ is significantly dependent on
the decay formula in terms of isospin asymmetry and decay energy. We also
noticed that modified scaling law Brown formula estimates of half-lives agreed
comparatively better with the experiment as compared to others. Moreover, the
present investigation provides significant information on the stability of the
superheavy island considered for ongoing and/or future experiments.
