  The definition of the g-index is as arbitrary as that of the h-index, because
the threshold number g^2 of citations to the g most cited papers can be
modified by a prefactor at one's discretion, thus taking into account more or
less of the highly cited publications within a dataset. In a case study I
investigate the citation records of 26 physicists and show that the prefactor
influences the ranking in terms of the generalized g-index less than for the
generalized h-index. I propose specifically a prefactor of 2 for the g-index,
because then the resulting values are of the same order of magnitude as for the
common h-index. In this way one can avoid the disadvantage of the original
g-index, namely that the values are usually substantially larger than for the
h-index and thus the precision problem is substantially larger; while the
advantages of the g-index over the h-index are kept. Like for the generalized
h-index, also for the generalized g-index different prefactors might be more
useful for investigations which concentrate only on top scientists with high
citation frequencies or on junior researchers with small numbers of citations.
