  This paper investigated the viable traversable wormhole solutions through
Karmarkar condition in the context of $f(\mathcal{G},T)$ theory. A static
spherical spacetime with anisotropic matter configuration is used to study the
wormhole geometry. Karmarkar condition is used to develop a viable shape
function for a static wormhole structure. A wormhole geometry is constructed
using the resulting shape function that satisfies all the required conditions
and connects the asymptotically flat regions of the spacetime. To assess the
viability of traversable wormhole geometries, the energy conditions are
analyzed by various models of this theory. Further, their stable state is
investigated through sound speed and adiabatic index. This investigation
demonstrates the presence of viable traversable wormhole solutions in the
modified theory.
