The catalog of galaxy clusters obtained by an adaptive matched filter method applied to the Sloan Digital Sky Survey Data Release Six

We present a catalog of galaxy clusters detected by running an adaptive matched filter finder on Sloan Digital Sky Survey Data Release 6. We present the position, redshift, richness, radius and core radius of these optically determined clusters, as well as error estimates on these values. The advantages of using a finder that does not make assumptions about the colors of the constituent galaxies in a cluster are demonstrated through comparisons with other cluster catalogs derived from SDSS data. We also compare our clusters with known X--ray clusters in overlapping regions of the sky, and we find reasonable correlations between our optical observables and X--ray observables.;From our catalog and available SDSS data, we also present a list of brightest cluster galaxy (BCG) candidates for each cluster in the form of the three brightest galaxies in the r-band. Properties of these BCGs are compared with expected values from simulations and earlier observations. Our findings are in good agreement with the current understanding of these galaxies.;We also examine BCGs for evidence of star formation. The types of galaxies that serve as BCGs are giant ellipticals, and are generally thought to be "red and dead." Cooling flows in clusters can deposit gas into a BCG. We find evidence for star formation in about 20% of our BCGs.;Our catalog can also serve as a basis for choosing future targets for X--ray, ultraviolet, and Sunyaev-Zel'dovich studies. We provide the most extensive list to-date of optical clusters for potential research in other bands.