Traversable wormholes in General Relativity (GR) require exotic matter
sources that violate the null energy condition (NEC), and such behavior may be
avoided in modified gravity. Moreover, the concept of non-commutative geometry
as a gravitational source can be leveraged both in GR and modified gravity to
realize non-trivial space-time configurations. In this study, we use $f(R)$
gravity in conjunction with non-commutative geometry to analyze spherically
symmetric traversable Morris-Thorne wormhole solutions from the aspect of
energy condition violation, considering both constant and variable red-shift
functions. First, we use well constrained metric and model parameters in a
viable $f(R)$ gravity model to demonstrate that wormholes respecting the NEC
can be obtained with suitable choices of parameters. Additionally, we check the
strong and dominant energy conditions to further validate our results. We then
leverage non-commutative geometry in the framework of $f(R)$ gravity to show
that wormholes respecting the different energy conditions with a phantom-like
source can be realized with suitable choices of model parameters. Our
comprehensive analyses using well-constrained model parameters show that
wormholes satisfying the NEC can be realized in the framework of
non-commutative geometry with modified gravity.
