This paper presents a study on the stability and properties of monolayer honeycomb structures of group IV elements and III-V binary compounds using first-principles plane wave calculations. The authors determine that 22 different honeycomb materials are stable and correspond to local minima on the Born-Oppenheimer surface. They find that binary compounds containing first-row elements (B, C, or N) have planar stable structures, while structures of Si, Ge, and other binary compounds are buckled due to puckering for stability. The band gaps calculated using Density Functional Theory with Local Density Approximation are corrected by the GW0 method. Si and Ge in honeycomb structures are semimetals with linear band crossing at the Fermi level, similar to graphene. All binary compounds are found to be semiconductors with band gaps depending on the constituent atoms. The authors also present a method to calculate elastic constants and Poisson's ratio for 2D honeycomb structures. Preliminary results suggest that these materials can offer new alternatives for nanoscale electronic devices. The study also reveals interesting correlations among the calculated properties of these honeycomb structures, similar to those of three-dimensional group IV and III-V compound semiconductors. The paper includes detailed analysis of phonon modes, mechanical properties, electronic band structures, and heterostructures of these materials. The results show that these honeycomb structures have unique electronic, mechanical, and optical properties that could be useful for various applications in nanotechnology and electronics.This paper presents a study on the stability and properties of monolayer honeycomb structures of group IV elements and III-V binary compounds using first-principles plane wave calculations. The authors determine that 22 different honeycomb materials are stable and correspond to local minima on the Born-Oppenheimer surface. They find that binary compounds containing first-row elements (B, C, or N) have planar stable structures, while structures of Si, Ge, and other binary compounds are buckled due to puckering for stability. The band gaps calculated using Density Functional Theory with Local Density Approximation are corrected by the GW0 method. Si and Ge in honeycomb structures are semimetals with linear band crossing at the Fermi level, similar to graphene. All binary compounds are found to be semiconductors with band gaps depending on the constituent atoms. The authors also present a method to calculate elastic constants and Poisson's ratio for 2D honeycomb structures. Preliminary results suggest that these materials can offer new alternatives for nanoscale electronic devices. The study also reveals interesting correlations among the calculated properties of these honeycomb structures, similar to those of three-dimensional group IV and III-V compound semiconductors. The paper includes detailed analysis of phonon modes, mechanical properties, electronic band structures, and heterostructures of these materials. The results show that these honeycomb structures have unique electronic, mechanical, and optical properties that could be useful for various applications in nanotechnology and electronics.