Argthtjtr

I was trying to recreate

Here is my MWE

documentclass{standalone}

usepackage{tkz-graph}

usepackage{tkz-berge}

definecolor{iceberg}{rgb}{0.44, 0.65, 0.82}

tikzstyle{VertexStyle} = [shape = circle, fill=iceberg,

minimum size = 6pt,

draw]

renewcommand*{VertexInnerSep}{8pt}

SetVertexLabelSetVertexMath

begin{document}



begin{minipage}{0.6textwidth}

begin{tikzpicture}[scale=0.4,rotate=90]

grGeneralizedPetersen[Math,prefix=u,RA=7,RB=4]{5}{2}

end{tikzpicture}

end{minipage}

begin{minipage}{0.6textwidth}

begin{tikzpicture}[scale=0.4]% 

grPetersen[form=2,prefix=v,RA=7,RB=3]%

end{tikzpicture}

end{minipage}

end{document}  

Just with the right node labels and font …

documentclass[border=5pt,tikz]{standalone}

usetikzlibrary{backgrounds}

usepackage{mathpazo}

definecolor{iceberg}{rgb}{0.44, 0.65, 0.82}

tikzset{

    every node/.style={

        fill=iceberg!40,draw,circle,minimum width=.5cm,font=Large

    }

}

begin{document}

    begin{tikzpicture}

        foreach x in {0,72,...,288}

        {

            pgfmathsetmacroindex{x/72+6}

            begin{pgfonlayer}{background}

                draw (x+18:2) -- (x+2*72+18:2);

                draw (x+18:5) -- (x+72+18:5);

                draw (x+18:2) -- (x+18:5);

            end{pgfonlayer}

                node at (x+3*72+18:2) {$u_{pgfmathprintnumberindex}$};

            pgfmathsetmacronindex{5-x/72}

                node at (x+3*72+18:5) {$u_{pgfmathprintnumbernindex}$};

        }

        begin{scope}[xshift=12cm]

            foreach x in {0,60,...,300}

            {

                pgfmathsetmacroindex{6-x/60}

                begin{pgfonlayer}{background}

                    draw[rotate=30] (x:5) -- (x+60:5);

                    foreach x in {-30,90,210}

                    {

                        draw (x:5) -- (0,0);

                    }

                end{pgfonlayer}

                node at (x+30+3*60:5) {$v_{pgfmathprintnumberindex}$};

            }

            foreach x in {0,120,240}

            {

                pgfmathsetmacroindex{9-x/120}

                    node at (x-30:2.5) {$v_{pgfmathprintnumberindex}$};

                begin{pgfonlayer}{background}

                    draw (x-30:2.5) to[bend left=30] (x-30+180:5);

                end{pgfonlayer}

                node at (0,0) {$v_{10}$};

            }

        end{scope}

    end{tikzpicture}

end{document}

Output:

Is this okay?

documentclass[border=3mm]{standalone}

usepackage{tkz-graph}

usepackage{tkz-berge}

definecolor{iceberg}{rgb}{0.44, 0.65, 0.82}

tikzstyle{VertexStyle} = [shape = circle, fill=iceberg,

minimum size = 8pt,

draw]

renewcommand*{VertexInnerSep}{8pt}

SetVertexLabelSetVertexMath

makeatletter

newcommand*{grPetersenm}[1]{%

begingroup%

    setkeys[GR]{cl}{#1}%

         grCycle[#1]{6}

         begin{scope}[rotate=120]

            edeftkzb@rtemp{cmdGR@cl@RB}

            edeftkzb@ptemp{cmdGR@cl@prefixx}

            grStar[#1,RA=tkzb@rtemp,prefix=tkzb@ptemp]{4}

          end{scope}

          setcounter{tkz@gr@a}{2}

          foreach V@x in  {0,...,5}{%

             ifthenelse{equal{thetkz@gr@a}{-1}}{%

                setcounter{tkz@gr@a}{2}}{%

                }%

                ifoddV@x

                 tikzset{EdgeStyle/.append style = {bend right}}fi

                Edge(cmdGR@cl@prefixV@x)(cmdGR@cl@prefixxthetkz@gr@a)

                addtocounter{tkz@gr@a}{-1}%

             }%

endgroup%

}

makeatother

begin{document}

begin{tikzpicture}[scale=0.7,rotate=90]

grGeneralizedPetersen[Math,prefix=u,RA=7,RB=4]{5}{2}

end{tikzpicture}

begin{tikzpicture}[scale=0.7,rotate=90]% 

grPetersenm[prefix=v,RA=7,RB=3]%

end{tikzpicture}

end{document}

EDIT

Changing the labels involve redefining few more macros. I think tikz-only solution would be easier. You can try something like this:

documentclass[border=3mm]{standalone}

usepackage{tikz}

definecolor{iceberg}{rgb}{0.44, 0.65, 0.82}

tikzstyle{VertexStyle} = [shape = circle, fill=iceberg,minimum size = 8mm,draw]

tikzstyle{EdgeStyle} = [line width=1pt]

begin{document}

begin{tikzpicture}[scale=0.7,rotate=90]

draw[EdgeStyle] (287:4cm) node[VertexStyle](u10){$u_{10}$} -- ++(287:4cm) node[VertexStyle](u1){$u_1$};

draw[EdgeStyle] (0:4cm)   node[VertexStyle](u9){$u_9$} -- ++(0:4cm) node[VertexStyle](u2){$u_2$};

draw[EdgeStyle] (72:4cm)  node[VertexStyle](u8){$u_8$} -- ++(72:4cm) node[VertexStyle](u3){$u_3$};

draw[EdgeStyle] (144:4cm) node[VertexStyle](u7){$u_7$} -- ++(144:4cm) node[VertexStyle](u4){$u_4$};

draw[EdgeStyle] (215:4cm) node[VertexStyle](u6){$u_6$} -- ++(215:4cm) node[VertexStyle](u5){$u_5$};

draw[EdgeStyle] (u1) -- (u2) -- (u3) -- (u4) -- (u5)--(u1);

draw[EdgeStyle] (u6) -- (u8) -- (u10) -- (u7) -- (u9)--(u6);

end{tikzpicture}



begin{tikzpicture}[scale=0.7,rotate=0]

draw[EdgeStyle] (300:8cm) node[VertexStyle](v1){$v_{1}$} -- (0:8cm) node[VertexStyle](v2){$v_{2}$} --  (60:8cm) node[VertexStyle](v3){$v_{3}$} -- (120:8cm) node[VertexStyle](v4){$v_{4}$} -- (180:8cm) node[VertexStyle](v5){$v_{5}$} -- (240:8cm) node[VertexStyle](v6){$v_{6}$} --cycle;

draw[EdgeStyle]  (0:0cm) node[VertexStyle](v10){$v_{10}$} -- (0:4cm) node[VertexStyle](v8){$v_{8}$} -- (v2);

draw[EdgeStyle]  (v10) -- (0:4cm) node[VertexStyle](v8){$v_{8}$} -- (v2);

draw[EdgeStyle]  (v10) -- (120:4cm) node[VertexStyle](v9){$v_{9}$} -- (v4);

draw[EdgeStyle]  (v10) -- (240:4cm) node[VertexStyle](v7){$v_{7}$} -- (v6);

draw[EdgeStyle]  (v5) edge[bend right] (v8);

draw[EdgeStyle]  (v3) edge[bend right] (v7);

draw[EdgeStyle]  (v1) edge[bend right] (v9);

end{tikzpicture}

end{document}