This study investigates the interaction and charge transfer between graphene and various metal substrates using first-principles density functional theory (DFT) calculations. The results show that graphene adsorbed on Al, Ag, Cu, Au, and Pt(111) surfaces exhibits weak bonding, preserving its unique electronic structure. However, charge transfer occurs, shifting the Fermi level relative to the conical points. The crossover from p-type to n-type doping occurs when the metal's work function is approximately 5.4 eV, which is higher than that of free-standing graphene (4.5 eV). A simple analytical model is developed to describe the Fermi level shift in terms of the metal's work function. Graphene interacts more strongly with Co, Ni, Pd, and Ti, leading to chemisorption and hybridization between graphene's p_z states and the metal's d-states, which opens a band gap in graphene and reduces its work function. In current-in-plane device geometries, this leads to n-type doping of graphene. The study also shows that the interaction between graphene and metal substrates can be divided into two classes: chemisorption (strong bonding on Co, Ni, Pd, and Ti) and physisorption (weak bonding on Al, Ag, Cu, Au, and Pt). Physisorbed graphene experiences a shift in the Fermi level due to charge transfer, which can be described by a model involving the interface dipole and potential step. The model predicts the Fermi level shift and work function changes based on the metal's work function and the graphene-metal separation. The results indicate that the doping of graphene depends on the metal's work function and the strength of the interaction. For chemisorbed graphene on Ni, Co, Pd, and Ti, the work function of the metal is significantly lowered, leading to n-type doping. The study also highlights the sensitivity of the results to the choice of density functional and the importance of considering the metal's lattice parameters and the graphene-metal separation in the calculations. The findings provide a comprehensive understanding of the electronic and structural properties of graphene on different metal substrates, which is crucial for the development of graphene-based electronic devices.This study investigates the interaction and charge transfer between graphene and various metal substrates using first-principles density functional theory (DFT) calculations. The results show that graphene adsorbed on Al, Ag, Cu, Au, and Pt(111) surfaces exhibits weak bonding, preserving its unique electronic structure. However, charge transfer occurs, shifting the Fermi level relative to the conical points. The crossover from p-type to n-type doping occurs when the metal's work function is approximately 5.4 eV, which is higher than that of free-standing graphene (4.5 eV). A simple analytical model is developed to describe the Fermi level shift in terms of the metal's work function. Graphene interacts more strongly with Co, Ni, Pd, and Ti, leading to chemisorption and hybridization between graphene's p_z states and the metal's d-states, which opens a band gap in graphene and reduces its work function. In current-in-plane device geometries, this leads to n-type doping of graphene. The study also shows that the interaction between graphene and metal substrates can be divided into two classes: chemisorption (strong bonding on Co, Ni, Pd, and Ti) and physisorption (weak bonding on Al, Ag, Cu, Au, and Pt). Physisorbed graphene experiences a shift in the Fermi level due to charge transfer, which can be described by a model involving the interface dipole and potential step. The model predicts the Fermi level shift and work function changes based on the metal's work function and the graphene-metal separation. The results indicate that the doping of graphene depends on the metal's work function and the strength of the interaction. For chemisorbed graphene on Ni, Co, Pd, and Ti, the work function of the metal is significantly lowered, leading to n-type doping. The study also highlights the sensitivity of the results to the choice of density functional and the importance of considering the metal's lattice parameters and the graphene-metal separation in the calculations. The findings provide a comprehensive understanding of the electronic and structural properties of graphene on different metal substrates, which is crucial for the development of graphene-based electronic devices.