  We investigate the attosecond transient absorption spectroscopy (ATAS) of
graphene by numerically solving four-band density-matrix equations, which
demonstrates apparent fish bone resonance structures. To gain insight into
these interesting structures, we exploit a simplified model that only considers
the electrons of $\Gamma$ and M points in the Brillouin zone. With the help of
this model, we can analytically express the ATAS spectrum as the sum of zeroth-
and first-order Bessel functions in the variables of the strength and frequency
of the infrared pump field as well as the effective mass of electrons at the
$\Gamma$ and M points. Lorentzian and Fano line shapes in the absorption
spectrum are addressed. The fish bone structure consists of periodic V-shaped
structure that can be explained by first-order Bessel functions and its tilt
angle is solely determined by the frequency of the pump laser. The periodicity
of the V-shaped structure in the fish bone originates from the periodic
dependence of the Lorentzian and Fano line shapes of the absorption spectrum on
the time delay between the pump and probe lasers. Compared with the numerical
results, our analytical theory can qualitatively or even quantitatively predict
the zeroth- and first-order fringes in the fish bone structures of the ATAS
spectrum. The gauge issues in the numerical simulations are also discussed.
