This paper presents first-principles calculations showing that silicon (Si) and germanium (Ge) can form stable, two-dimensional (2D), low-buckled honeycomb structures. These structures are similar to graphene, with charge carriers behaving like massless Dirac fermions due to linearly crossed π and π* bands at the Fermi level. Both bare and hydrogen-passivated nanoribbons of Si and Ge exhibit size and orientation-dependent electronic and magnetic properties, making them promising for nanodevice applications. The study uses density functional theory (DFT) to analyze the stability of these structures. Phonon dispersion calculations show that the low-buckled (LB) honeycomb structures of Si and Ge are stable, with well-separated acoustic and optical branches and positive frequencies. The LB structures of Si and Ge have linear band crossings at the K and K' points of the hexagonal Brillouin zone, indicating Dirac points. These structures are more stable than high-buckled (HB) structures, which are not real local minima. The electronic band structures of LB Si and Ge show semimetallic behavior with π and π* bands crossing at the Fermi level. The Fermi velocity is estimated to be around 10^6 m/s, similar to graphene. These materials are ambipolar, with electronic properties dependent on their size and geometry. The band gap of Si and Ge nanoribbons varies with width, showing oscillatory behavior, and can be modified by hydrogen passivation. The study also examines the electronic and magnetic properties of Si and Ge nanoribbons. Armchair and zigzag nanoribbons exhibit different electronic behaviors, with hydrogen passivation affecting their band gaps. The magnetic properties of these nanoribbons depend on their structure and edge termination. The results suggest that Si and Ge can form stable 2D honeycomb structures with properties similar to graphene, offering potential for future nanodevice applications.This paper presents first-principles calculations showing that silicon (Si) and germanium (Ge) can form stable, two-dimensional (2D), low-buckled honeycomb structures. These structures are similar to graphene, with charge carriers behaving like massless Dirac fermions due to linearly crossed π and π* bands at the Fermi level. Both bare and hydrogen-passivated nanoribbons of Si and Ge exhibit size and orientation-dependent electronic and magnetic properties, making them promising for nanodevice applications. The study uses density functional theory (DFT) to analyze the stability of these structures. Phonon dispersion calculations show that the low-buckled (LB) honeycomb structures of Si and Ge are stable, with well-separated acoustic and optical branches and positive frequencies. The LB structures of Si and Ge have linear band crossings at the K and K' points of the hexagonal Brillouin zone, indicating Dirac points. These structures are more stable than high-buckled (HB) structures, which are not real local minima. The electronic band structures of LB Si and Ge show semimetallic behavior with π and π* bands crossing at the Fermi level. The Fermi velocity is estimated to be around 10^6 m/s, similar to graphene. These materials are ambipolar, with electronic properties dependent on their size and geometry. The band gap of Si and Ge nanoribbons varies with width, showing oscillatory behavior, and can be modified by hydrogen passivation. The study also examines the electronic and magnetic properties of Si and Ge nanoribbons. Armchair and zigzag nanoribbons exhibit different electronic behaviors, with hydrogen passivation affecting their band gaps. The magnetic properties of these nanoribbons depend on their structure and edge termination. The results suggest that Si and Ge can form stable 2D honeycomb structures with properties similar to graphene, offering potential for future nanodevice applications.