  It is known that static traversable wormhole in Einstein gravity is supported
by matter that violates null energy conditions (NEC). Essentially such wormhole
will be characterised by a central throat with anisotropic matter lining the
throat that violates NEC. This in turn provides viable geometry for the
wormhole to sustain. In 2018, L. Herrera introduced a new classification for
spherically symmetric bodies called ``complexity factor". It was proposed that
a spherically symmetric non trivial geometry can be classified as complex or
non-complex based on the nature of the inhomogeneity and anisotropy of the
stress energy tensors with only homogeneous and isotropic matter distribution
leading to null complexity. Mathematically there was also another way of
obtaining zero complexity geometry. In this context since static traversable
wormhole by default is characterised by anisotropic and inhomogeneous matter
stress tensors, the question we answer is whether it is possible to obtain zero
complexity class of wormholes supported by exotic matter.
