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Wormhole solutions in General Relativity (GR) require \textit{exotic} mattersources that violate the null energy condition (NEC), and it is well known thathigher-order modifications of GR and some alternative matter sources cansupport wormholes. In this study, we explore the possibility of formulatingtraversable wormholes in $f(R)$ modified gravity, which is perhaps the mostwidely discussed modification of GR, with two approaches. First, to investigatethe effects of geometrical constraints on the global characteristics, we gaugethe $rr$-component of the metric tensor, and employ Pad\`{e} approximation tocheck whether a well-constrained \textit{shape function} can be formulated inthis manner. We then derive the field equations with a background of stringcloud, and numerically analyse the energy conditions, stability, and amount ofexotic matter in this space-time. Next, as an alternative source in a simple$f(R)$ gravity model, we use the background cloud of strings to estimate thewormhole shape function, and analyse the relevant properties of the space-time.These results are then compared with those of wormholes threaded by normalmatter in the simple $f(R)$ gravity model considered. The results demonstratethat wormholes with NEC violations are feasible; however, the wormholespace-times in the simple $f(R)$ gravity model are unstable.

Traversable wormholes in $f(R)$ gravity sourced by a cloud of strings