  This paper investigates static spherically symmetric traversable wormhole
solutions in $f(\mathcal{G},T)$ gravity ($\mathcal{G}$ and $T$ represent the
Gauss-Bonnet invariant and trace of the energy-momentum tensor, respectively).
We construct explicit expressions for ordinary matter by taking specific form
of red-shift function and $f(\mathcal{G},T)$ model. To analyze possible
existence of wormholes, we consider anisotropic, isotropic as well as
barotropic matter distributions. The graphical analysis shows the violation of
null energy condition for the effective energy-momentum tensor throughout the
evolution while ordinary matter meets energy constraints in certain regions for
each case of matter distribution. It is concluded that traversable WH solutions
are physically acceptable in this theory.
