The form of the Latin name of a constellation used when describing objects, especially
stars, within that constellation. For example, the genitive form of 'Centaurus' is
'Centauri'; hence the famous 'Alpha Centauri', the
brightest star in that
Strictly genitive refers to the grammatical case used to denote possession or association. In English this is commonly denoted by the word 'of', but in Latin the case is indicated by inflection; that is, a change to the ending of the word in question. This rule holds for the Latin names given to the constellations, so, following the example above, 'Alpha Centauri' literally means 'Alpha (the brightest star) of Centaurus'.
The most familiar use of genitive constellation names is in Bayer desginations, which use Greek letters to rank the stars of a constellation - at least theoretically - by magnitude, followed by the genitive case of the constellation's name. 'Alpha Centauri' is a famous example of this system, as are names like 'Epsilon Eridani' (the Epsilon star of Eridanus, the River, now officially named 'Ran') or 'Tau Ceti' (the Tau star of Cetus, the Whale), and so on.
Genitive constellation names are also used by the Flamsteed system, which uses numbers instead of Greek letters, counting west to east across the constellation. For example, the brilliant star Sirius is designated 'Alpha Canis Majoris' on the Bayer system, and also '9 Canis Majoris' by the Flamsteed numbers (that is, the ninth Flamsteed star from the western boundary of Canis Major). Genitives are also used in variable designations (such as 'UV Ceti') and very occasionally in the proper names of stars such as Proxima Centauri or Mira Ceti.
Each constellation has an official abbreviation of its name, and it is common to see this used in place of the full genitive form. For example, the first confirmed extrasolar planet to be discovered orbits a star designated in full '51 Pegasi' (that is, fifty-first of the eighty-nine Flamsteed stars in the constellation Pegasus). In practice, this star is almost universally referred to as simply '51 Peg' (or more recently by the official proper name of Helvetios).
The table below lists the genitive forms and abbreviations for all eighty-eight officially recognised constellations. There are two cases (Camelopardalis and Puppis) where the genitive form remains the same as the constellation name; in all other cases the ending of the name changes to form the genitive.