The effect of Holstein phonons on the electrical conductivity of doped monolayer graphene

•Theoretical calculation of electrical conductance of monolayer graphene in the context of Holstein model.•The investigation of electrical conductance versus electron–phonon coupling strengths.•The investigation of electrical conductance versus electronic concentration.

Electrical conductivity of graphene sheets is studied in the presence of coupling between lattice optical vibrations and electrons. Green's function approach is implemented to find the temperature behavior of electrical conductivity. Moreover, the effect of electronic doping on the electrical conductivity of graphene with electron–phonon interaction is investigated. Our results show that electrical conductivity increases as a function of temperature at low temperature and gets a maximum value and then decays at high temperature.