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This paper uses the Noether symmetry approach to examine the viable andstable traversable wormhole solutions in the framework of$f(\mathcal{R,}\mathcal{T}^{2})$ theory, where $\mathcal{R}$ is the Ricciscalar and $\mathcal{T}^{2}=\mathcal{T}_{\mu\nu}\mathcal{T}^{\mu\nu}$ is theself-contraction of stress-energy tensor. For this purpose, we consider aspecific model of this modified theory to obtain exact solutions of the Noetherequations. Further, we formulate the generators of Noether symmetry and firstintegrals of motion. We analyze the presence of viable and stable traversablewormhole solutions corresponding to different redshift functions. In order todetermine whether this theory provides physically viable and stable wormholegeometry or not, we check the graphical behavior of null energy constraint,causality condition and adiabatic index for effective stress-energy tensor. Itis found that viable and stable traversable wormhole solutions exist in thismodified theory.

Traversable Wormhole Solutions admitting Noether Symmetry in $f(\mathcal{R,}\mathcal{T}^{2})$ Theory