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The objective of this paper is to investigate the existence and stability of wormholes within the framework of modified gravity, specifically F(R,Lm)gravity, where F(R)represents a function of the Ricci scalar and Lmaccounts for matter Lagrangian. We consider the linear functional form of F(R,Lm)with two novel shape functions. To illustrate the wormhole configurations, the embedding diagram in two and three-dimensional Euclidean space is also examined. The Tolman–Oppenheimer–Volkoff (TOV) equation is also used to investigate the stability of the created framework of the traversable wormholes. We observed that near the wormhole throat, the complexity factor (ycf) is monotonically decreasing for wormhole Model-I and increasing for wormhole Model-II, and for higher values of the radial coordinate, ycfis getting closer to zero. Our analysis shows that the energy conditions have been violated and that this generic violation points to the presence of exotic matter.

This paper investigates the characteristics of wormhole solutions within the framework of Rastall gravity. First, we derived the shape functions using two different equations of state (EoS). Then we examined the essential characteristics of the shape function for wormholes and the behavior of energy conditions. The present investigation based on the EoS produces wormhole solutions valid for negative values of μor Υ, where μ=κΥis a dimensionless parameter and Υdenotes a Rastall parameter. Furthermore, the Rastall parameter Υplays a vital role in the stability conditions and geometric properties of a wormhole. The volume integral quantifier (VIQ) is also discussed, which gives the idea of the amount of exotic matter required near the wormhole throat. The conclusion shows that our solutions derived using both EoS in Rastall gravity are physically feasible.