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The current study explores the generalized embedded wormhole solutions in thebackground of $f(\mathcal{R},\mathcal{G})$ gravity, where $\mathcal{R}$represents the Ricci scalar and $\mathcal{G}$ denotes the Gauss-Bonnetinvariant. To investigate the necessary structures of the wormhole solutions wethoroughly analyzed the energy conditions under $f(\mathcal{R},\mathcal{G})$gravity within the anisotropic source of matter. To meet this aim, we considerspherically symmetric geometry with the most generic gravity model of thegravity. A modified version of the field equations is calculated for twodifferent embedded wormhole solutions. All the energy conditions are calculatedand shown graphically with the regional ranges of the model parameter. Further,the invalid region of the energy conditions confirms the presence of exoticmatter. Finally, we have concluding remarks.

Viable embedded wormholes and energy conditions in $f(\mathcal{R},\mathcal{G})$ gravity