g[x_,y_]:=(1/(2*π*(σ^2)))*(E^(-(((x^2)+(y^2))/(2*(σ^2)))))/.{σ->1};

Column[{
Plot3D[g[x,y],{x,-4,4},{y,-4,4},AxesLabel->{"x","y"},PlotRange->All,ImageSize->450,BaseStyle->{FontSize->14},PlotLegends->{"(Subscript[G, 1])(x,y)"},PlotPoints->100],
DensityPlot[g[x,y],{x,-4,4},{y,-4,4},ColorFunction->GrayLevel,PlotRange->All,BaseStyle->{FontSize->14},FrameLabel->{"x","y"},PlotLegends->Automatic,ImageSize->Medium,PlotPoints->100]
},Center
]