ClearAll["Global`*"]
SetOptions[ParametricPlot,BaseStyle->{FontFamily->"Times New Roman",FontSize->20}, FrameTicks->Automatic, FrameTicksStyle->Directive[Black,20], Ticks->None, Frame->{True,True,False,False}, PlotStyle->Directive[Thickness[0.001]]];
gc=2.0;
gf=0.2;
LStar =gf*gc/((gf-gc)^2)
tStar = gf/(3*(gc-2*gf)^3)*(8*gf*gf *(gf-gc)+6*(gc-2*gf)*(gc^2 - 2*gf*gc+2*gf^2)*LStar - 3*(gc-2*gf)^2*gf*LStar^2 +8*(gc-gf)*gf^(0.5)*(gf+LStar*(2*gf-gc))^(1.5));
graph11=ParametricPlot[{Lc,((gc-2*gf)^2)/(2*gf*(gc^2 + 2*gf^2 *(1+Lc) - gc*gf*(2+Lc)+2*gf^(0.5)*(gf-gc)*Sqrt[gf+Lc*(2*gf-gc)]))},{Lc,0,LStar},PlotStyle->Blue];
graph21 = ParametricPlot[{Lc,1/(2*gc*Lc)},{Lc,LStar,1.5},PlotStyle->Blue];
gf=0.4;
LStar =gf*gc/((gf-gc)^2)
tStar = gf/(3*(gc-2*gf)^3)*(8*gf*gf *(gf-gc)+6*(gc-2*gf)*(gc^2 - 2*gf*gc+2*gf^2)*LStar - 3*(gc-2*gf)^2*gf*LStar^2 +8*(gc-gf)*gf^(0.5)*(gf+LStar*(2*gf-gc))^(1.5));
graph12=ParametricPlot[{Lc,((gc-2*gf)^2)/(2*gf*(gc^2 + 2*gf^2*(1+Lc) - gc*gf*(2+Lc)+2*gf^(0.5)*(gf-gc)*Sqrt[gf+Lc*(2*gf-gc)]))},{Lc,0,LStar},PlotStyle->Red];
graph22 = ParametricPlot[{Lc,1/(2*gc*Lc)},{Lc,LStar,1.5},PlotStyle->Red];
gf=0.6;
LStar =gf*gc/((gf-gc)^2)
tStar = gf/(3*(gc-2*gf)^3)*(8*gf*gf *(gf-gc)+6*(gc-2*gf)*(gc^2 - 2*gf*gc+2*gf^2)*LStar - 3*(gc-2*gf)^2*gf*LStar^2 +8*(gc-gf)*gf^(0.5)*(gf+LStar*(2*gf-gc))^(1.5));
graph13=ParametricPlot[{Lc,((gc-2*gf)^2)/(2*gf*(gc^2 + 2*gf^2 *(1+Lc) - gc*gf*(2+Lc)+2*gf^(0.5)*(gf-gc)*Sqrt[gf+Lc*(2*gf-gc)]))},{Lc,0,LStar},PlotStyle->Black];
graph23 = ParametricPlot[{Lc,1/(2*gc*Lc)},{Lc,LStar,1.5},PlotStyle->Black];
gf=0.8;
LStar =gf*gc/((gf-gc)^2)
tStar = gf/(3*(gc-2*gf)^3)*(8*gf*gf *(gf-gc)+6*(gc-2*gf)*(gc^2 - 2*gf*gc+2*gf^2)*LStar - 3*(gc-2*gf)^2*gf*LStar^2 +8*(gc-gf)*gf^(0.5)*(gf+LStar*(2*gf-gc))^(1.5));
graph14=ParametricPlot[{Lc,((gc-2*gf)^2)/(2*gf*(gc^2 + 2*gf^2*(1+Lc) - gc*gf*(2+Lc)+2*gf^(0.5)*(gf-gc)*Sqrt[gf+Lc*(2*gf-gc)]))},{Lc,0,LStar},PlotStyle->Green];
graph24 = ParametricPlot[{Lc,1/(2*gc*Lc)},{Lc,LStar,1.5},PlotStyle->Green];
Show[graph21,graph11,graph12,graph22,graph23,graph13,graph14,graph24,PlotRange->All,AspectRatio->1]

ClearAll["Global`*"]
SetOptions[ParametricPlot,BaseStyle->{FontFamily->"Times New Roman",FontSize->20}, FrameTicks->Automatic, FrameTicksStyle->Directive[Black,20], Ticks->None, Frame->{True,True,False,False}, PlotStyle->Directive[Thickness[0.01]]];
gc=0.5;
gf=0.3;
LStar =gf*gc/((gf-gc)^2)
tStar = gf/(3*(gc-2*gf)^3)*(8*gf*gf *(gf-gc)+6*(gc-2*gf)*(gc^2 - 2*gf*gc+2*gf^2)*LStar - 3*(gc-2*gf)^2*gf*LStar^2 +8*(gc-gf)*gf^(0.5)*(gf+LStar*(2*gf-gc))^(1.5));
graph11=ParametricPlot[{Lc,1/gf},{Lc,0,LStar},PlotStyle->Blue];
graph21 = ParametricPlot[{Lc,1/gf*(1-Sqrt[(1-gf/gc)^2-gf/(gc*Lc)])},{Lc,LStar,100},PlotStyle->Blue];
gf=0.4;
LStar =gf*gc/((gf-gc)^2)
tStar = gf/(3*(gc-2*gf)^3)*(8*gf*gf *(gf-gc)+6*(gc-2*gf)*(gc^2 - 2*gf*gc+2*gf^2)*LStar - 3*(gc-2*gf)^2*gf*LStar^2 +8*(gc-gf)*gf^(0.5)*(gf+LStar*(2*gf-gc))^(1.5));
graph12=ParametricPlot[{Lc,1/gf},{Lc,0,LStar},PlotStyle->Red];
graph22 = ParametricPlot[{Lc,1/gf*(1-Sqrt[(1-gf/gc)^2-gf/(gc*Lc)])},{Lc,LStar,100},PlotStyle->Red];
gf=0.5;
graph13=ParametricPlot[{Lc,1/gf},{Lc,0,100},PlotStyle->Black];
gf=0.6;
LStar =gf*gc/((gf-gc)^2)
tStar = gf/(3*(gc-2*gf)^3)*(8*gf*gf *(gf-gc)+6*(gc-2*gf)*(gc^2 - 2*gf*gc+2*gf^2)*LStar - 3*(gc-2*gf)^2*gf*LStar^2 +8*(gc-gf)*gf^(0.5)*(gf+LStar*(2*gf-gc))^(1.5));
graph14=ParametricPlot[{Lc,1/gf},{Lc,0,100},PlotStyle->Green];
gf=0.7;
LStar =gf*gc/((gf-gc)^2)
tStar = gf/(3*(gc-2*gf)^3)*(8*gf*gf *(gf-gc)+6*(gc-2*gf)*(gc^2 - 2*gf*gc+2*gf^2)*LStar - 3*(gc-2*gf)^2*gf*LStar^2 +8*(gc-gf)*gf^(0.5)*(gf+LStar*(2*gf-gc))^(1.5));
graph15=ParametricPlot[{Lc,1/gf},{Lc,0,100},PlotStyle->Purple];
graph16=ParametricPlot[{Lc,(1+2*Lc)/(2*gc*Lc)},{Lc,0.5,100},PlotStyle->{Dotted,Black,Thickness[0.002]}];
Show[graph21,graph11,graph12,graph22,graph13,graph14,graph15,graph16,PlotRange->All,AspectRatio->1,PlotStyle->Directive[Thickness[0.02]]]
SetDirectory["C:\\Users\\admin\\Desktop"]
Export["ThroughputVsRho.eps",Show[graph21,graph11,graph12,graph22,graph13,graph14,graph15,graph16,PlotRange->All,AspectRatio->1,PlotStyle->Directive[Thickness[0.01]],Background->White,Axes->False]]