Is there a formula for absolute magnitude that does not contain an apparent magnitude term? I have a star that I need to calculate the absolute magnitude of. I am given the temperature, luminosity, radius, mass, and distance in light-years. So I am wondering, what is the formula to compute this, using only these terms?
Yes. You derive the absolute bolometric magnitude by reference to the Sun. The Sun has a bolometric magnitude (i.e. integrated over all wavelengths) of about 4.75. Thus the difference in bolometric magnitudes is given by the log of the ratio of luminosities like so
$$ M_{\rm bol} = 4.75 -2.5 \log_{10} \left(\frac{L_*}{L_{\odot}}\right)\ ,$$
where $L_{\odot} = 3.8\times 10^{26}$ W is the luminosity of the Sun and $L_*$ is the luminosity of the star.
To get the absolute visual magnitude then you need to subtract a bolometric correction, which to first order, depends on the temperature of the star (it also depends to second order on the composition and gravity).
$$ M_V = M_{\rm bol} - BC_V\ .$$
A table of bolometric corrections vs temperature can be found in the 6th column of this authoritative table, which is in common use by astronomers/astrophysicists.