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 = -0.056pm0.002 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 = -1.41pm0.05. 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 4pm 1 dE companions within a projected radius of 13.9h^{-1} kpc. (Abridged)
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