  We study the dwarf galaxy population in the central ~700 arcmin^2 of the Coma
cluster, the majority of which are early-type dwarf elliptical (dE) galaxies.
Analysis of the statistically-decontaminated dE galaxy sequence in the
color-magnitude diagram reveals a highly significant trend of color with
magnitude (\Delta (B-R)/\Delta R = -0.056\pm0.002 mag), in the sense that
fainter dEs are bluer and thus presumably more metal-poor. The mean color of
the faintest dEs in our sample is (B-R)~1.15 mag, consistent with a color
measurement of the diffuse intracluster light in the Coma core. This
intracluster light could then have originated from the tidal disruption of
faint dEs in the cluster core. The total galaxy luminosity function (LF) is
well modeled as the sum of a log-normal distribution for the giant galaxies,
and a Schechter function for the dE galaxies with a faint-end slope \alpha =
-1.41\pm0.05. This value of \alpha is consistent with those measured for the
Virgo and Fornax clusters. The spatial distribution of the faint dE galaxies
(19.0 < R \le 22.5 mag) has R_c = 22.15 arcmin (~0.46h^{-1} Mpc), significantly
larger than the R_c = 13.71 arcmin (~0.29h^{-1} Mpc) found for the cluster
giants and the brighter dEs (R \le 19.0 mag), consistent with tidal disruption
of the faint dEs. Finally, we find that most dEs belong to the general Coma
cluster potential rather than as satellites of individual giant galaxies: An
analysis of the number counts around 10 cluster giants reveals that they each
have on average 4\pm 1 dE companions within a projected radius of 13.9h^{-1}
kpc. (Abridged)
