  It has been recently observed that the conventional electron-phonon mediated
superconducting phase in graphene can be easily induced by doping its surface
with the lihitum adatoms. Due to the emerging interest in this field of
research we present our theoretical discussion of the thermodynamic properties
of this novel structures within the strong-coupling limit. We show, that
together with the increase of the adatom doping, from one (LiC$_{6}$) to two
(Li$_{2}$C$_{6}$) lithium atoms per unit cell, the critical temperature ($T_C$)
changes from 8.55 K to 21.83 K. Such trend is also observed for other
thermodynamic properties which moreover differ from the predictions of the
Bardeen-Cooper-Schrieffer theory. In particular, the zero-temperature energy
gap to the critical temperature ratio: R$_{\Delta}^{{\rm LiC}_6}$=3.72 and
R$_{\Delta}^{{\rm Li}_{2}{\rm C}_6}$=4.21; the ratio of the specific heat for
superconducting and the normal state: R$_{\rm C}^{{\rm LiC}_6}$=1.47 and
R$_{\rm C}^{{\rm Li}_{2}{\rm C}_6}$=1.79; and the parameter connected with the
zero-temperature thermodynamic critical field: R$_{\rm H}^{{\rm LiC}_6}$=0.167
and R$_{\rm H}^{{\rm Li}_{2}{\rm C}_6}$=0.144. Finally the electron effective
mass at $T_c$ is calculated to be: $(1.62m_e)_{{\rm LiC}_6}$ and
$(2.48m_e)_{{\rm Li}_{2}{\rm C}_6}$.
