  This work investigates some feasible regions for the existence of traversable
wormhole geometries in $f(R,G)$ gravity, where $R$ and $G$ represent the Ricci
scalar and the Gauss-Bonnet invariant respectively. Three different matter
contents anisotropic fluid, isotropic fluid and barotropic fluid have been
considered for the analysis. Moreover, we split $f(R,G)$ gravity model into
Strobinsky like $f(R)$ model and a power law $f(G)$ model to explore wormhole
geometries. We select red-shift and shape functions which are suitable for the
existence of wormhole solutions for the chosen $f(R,G)$ gravity model. It has
been analyzed with the graphical evolution that the null energy and weak energy
conditions for the effective energy-momentum tensor are usually violated for
the ordinary matter content. However, some small feasible regions for the
existence of wormhole solutions have been found where the energy conditions are
not violated. The overall analysis confirms the existence of the wormhole
geometries in $f(R,G)$ gravity under some reasonable circumstances.
