  This paper investigates the geometry of static traversable wormhole through
Noether symmetry approach in $f(R)$ gravity. We take perfect fluid distribution
and formulate symmetry generators with associated conserved quantities
corresponding to general form, power-law and exponential $f(R)$ models. In each
case, we evaluate wormhole solutions using constant and variable red-shift
functions. We analyze the behavior of shape function, viability of constructed
$f(R)$ model and stability of wormhole solutions graphically. The physical
existence of wormhole solutions can be examined through null/weak energy
conditions of perfect fluid and null energy condition of the effective
energy-momentum tensor. The graphical interpretation of constructed wormhole
solutions ensures the existence of physically viable and traversable wormholes
for all models. It is concluded that the constructed wormholes are found to be
stable in most of the cases.
