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We study the dynamics of test particle and stability of circular geodesics inthe gravitational field of a non-commutative geometry inspired Schwarzschildblack hole spacetime (NCSBH). The coordinate time Lyapunov exponent($\lambda_{c}$) is crucial to investigate the stability of equatorial circulargeodesics of massive and massless test particles. The stability or instabilityof circular orbits are discussed by analysing the variation of Lyapunovexponent with radius of these orbits for different values of non-commutativeparameter ($\alpha$). In the case of null circular orbits, the instabilityexponent is calculated and presented to discuss the instability of nullcircular orbits. Further, by relating parameters corresponding to null circulargeodesics (i.e. angular frequency and Lyapunov exponent), the quasinormal modes(QNMs) for a massless scalar field perturbation in the eikonal approximationare evaluated, and also visualised by relating the real and imaginary parts.The nature of scalar field potential, by varying the non-commutative parameter($\alpha$) and angular momentum of perturbation ($l$), are also observed anddiscussed.

Geodesic stability and quasinormal modes of non-commutative Schwarzschild black hole employing Lyapunov exponent