mjhjmtu

I was trying to recreate

Here is my MWE

documentclassstandalone
usepackagetkz-graph
usepackagetkz-berge
definecoloricebergrgb0.44, 0.65, 0.82
tikzstyleVertexStyle = [shape = circle, fill=iceberg,
minimum size = 6pt,
draw]
renewcommand*VertexInnerSep8pt
SetVertexLabelSetVertexMath
begindocument

beginminipage0.6textwidth
begintikzpicture[scale=0.4,rotate=90]
grGeneralizedPetersen[Math,prefix=u,RA=7,RB=4]52
endtikzpicture
endminipage
beginminipage0.6textwidth
begintikzpicture[scale=0.4]% 
grPetersen[form=2,prefix=v,RA=7,RB=3]%
endtikzpicture
endminipage
enddocument 

Just with the right node labels and font …

documentclass[border=5pt,tikz]standalone
usetikzlibrarybackgrounds
usepackagemathpazo
definecoloricebergrgb0.44, 0.65, 0.82
tikzset
 every node/.style=
 fill=iceberg!40,draw,circle,minimum width=.5cm,font=Large
 

begindocument
 begintikzpicture
 foreach x in 0,72,...,288
 
 pgfmathsetmacroindexx/72+6
 beginpgfonlayerbackground
 draw (x+18:2) -- (x+2*72+18:2);
 draw (x+18:5) -- (x+72+18:5);
 draw (x+18:2) -- (x+18:5);
 endpgfonlayer
 node at (x+3*72+18:2) $u_pgfmathprintnumberindex$;
 pgfmathsetmacronindex5-x/72
 node at (x+3*72+18:5) $u_pgfmathprintnumbernindex$;
 
 beginscope[xshift=12cm]
 foreach x in 0,60,...,300
 
 pgfmathsetmacroindex6-x/60
 beginpgfonlayerbackground
 draw[rotate=30] (x:5) -- (x+60:5);
 foreach x in -30,90,210
 
 draw (x:5) -- (0,0);
 
 endpgfonlayer
 node at (x+30+3*60:5) $v_pgfmathprintnumberindex$;
 
 foreach x in 0,120,240
 
 pgfmathsetmacroindex9-x/120
 node at (x-30:2.5) $v_pgfmathprintnumberindex$;
 beginpgfonlayerbackground
 draw (x-30:2.5) to[bend left=30] (x-30+180:5);
 endpgfonlayer
 node at (0,0) $v_10$;
 
 endscope
 endtikzpicture
enddocument

Output:

Is this okay?

documentclass[border=3mm]standalone
usepackagetkz-graph
usepackagetkz-berge
definecoloricebergrgb0.44, 0.65, 0.82
tikzstyleVertexStyle = [shape = circle, fill=iceberg,
minimum size = 8pt,
draw]
renewcommand*VertexInnerSep8pt
SetVertexLabelSetVertexMath
makeatletter
newcommand*grPetersenm[1]%
begingroup%
 setkeys[GR]cl#1%
 grCycle[#1]6
 beginscope[rotate=120]
 edeftkzb@rtempcmdGR@cl@RB
 edeftkzb@ptempcmdGR@cl@prefixx
 grStar[#1,RA=tkzb@rtemp,prefix=tkzb@ptemp]4
 endscope
 setcountertkz@gr@a2
 foreach V@x in 0,...,5%
 ifthenelseequalthetkz@gr@a-1%
 setcountertkz@gr@a2%
 %
 ifoddV@x
 tikzsetEdgeStyle/.append style = bend rightfi
 Edge(cmdGR@cl@prefixV@x)(cmdGR@cl@prefixxthetkz@gr@a)
 addtocountertkz@gr@a-1%
 %
endgroup%

makeatother
begindocument
begintikzpicture[scale=0.7,rotate=90]
grGeneralizedPetersen[Math,prefix=u,RA=7,RB=4]52
endtikzpicture
begintikzpicture[scale=0.7,rotate=90]% 
grPetersenm[prefix=v,RA=7,RB=3]%
endtikzpicture
enddocument

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
usepackagetikz
definecoloricebergrgb0.44, 0.65, 0.82
tikzstyleVertexStyle = [shape = circle, fill=iceberg,minimum size = 8mm,draw]
tikzstyleEdgeStyle = [line width=1pt]
begindocument
begintikzpicture[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);
endtikzpicture

begintikzpicture[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);
endtikzpicture
enddocument