  This work aims to investigate some possible emergence of relativistic compact
stellar objects in modified $f(\mathcal{G})$ gravity using Noether symmetry
approach. For this purpose, we assume static spherically symmetric spacetime in
the presence of isotropic matter distribution. We construct Noether symmetry
generators along with associated conserved quantities by considering the
standard choice of viable $f(\mathcal{G})$ gravity model i.e. $f(\mathcal{G})=
\alpha\mathcal{G}^{n}$, where $\alpha$ is the model parameter. In particular,
we use conservation relation acquired from the classical Noether approach by
imposing some appropriate initial conditions to construct the metric
potentials. The obtained conserved quantity play vital role in describing the
stellar structure of compact stars. Moreover, by considering an appropriate
numerical solution, some salient features of compact stellar structures like
effective energy density, pressure, energy conditions, stability against
equilibrium of the forces and speed of sound are discussed by assigning the
suitable values of model parameter involved. Our study reveals that the compact
objects in $f(\mathcal{G})$ gravity from Noether symmetry approach depend on
the conserved quantity obtained and the model parameter $\alpha$. In nutshell,
Noether symmetries are quite helpful to generate solutions that follow
physically accepted phenomena. Moreover, we observed that these obtained
solutions are consistent with the astrophysical observational data, which
depicts the viability of our proposed Noether symmetry scheme.
