  The isotopic compositions of ruthenium (Ru) are measured from presolar
silicon carbide (SiC) grains. In a popular scenario, the presolar SiC grains
formed in the outskirt of an asymptotic giant branch (AGB) star, left the star
as a stellar wind, and joined the presolar molecular cloud from which the solar
system formed. The Ru isotopes formed inside the star, moved to the stellar
surface during the AGB phase, and were locked into the SiC grains. Following
this scenario, we analyze the NuGrid data which provide the abundances of the
Ru isotopes in the stellar wind for a set of stars in a wide range of initial
masses and metallicities. We apply the C>O (carbon abundance larger than the
oxygen abundance) condition which is commonly adopted for the condition of the
SiC formation in the stellar wind. The NuGrid data confirm that SiC grains do
not form in the winds of massive stars. The isotopic compositions of Ru in the
winds of low-mass stars can explain measurements. We find that lower-mass stars
($1.65~M_\odot$ and $2~M_\odot$) with low metallicity (Z=0.0001) can explain
most of the measured isotopic compositions of Ru. We confirm that the abundance
of ${^{99}}$Ru inside the presolar grain includes the contribution from the
in-situ decay of ${^{99}}$Tc. We also verify our conclusion by comparing the
isotopic compositions of Ru integrated over all the pulses with those
calculated at individual pulses.
