I need help with latex tiKz code for drawing the graph

Question

I need some help with drawing this graph in LaTeX. The learning curve is quite steep!

Zarko · Accepted Answer

Like this:

for positions of dots are used corners of regular shape from the library shapes.geometric
dots and connection lines are drawn in the loops
labels of dots are defined with counters in the loop

documentclass[tikz, border=3mm]{standalone}
usetikzlibrary{shapes.geometric}

tikzset{
dot/.style = {circle, inner sep=1pt, fill,
              node contents={}},
 PG/.style = {% PentaGon
              regular polygon, regular polygon sides=5,
              minimum size=#1cm,
              node contents={}},
every label/.append style = {inner sep=1pt, font=tiny} 
        }

begin{document}
    begin{tikzpicture}
node (n1) [PG=6, draw];
node (n2) [PG=4];
node (n3) [PG=2];
%
foreach i/ii [evaluate=ii as jj using int(ii+5),
                 evaluate=ii as kk using int(ii+10)] 
            in {1/1,2/5,3/4,4/3,5/2}
{
    node at (n1.corner i) [dot, label=90+i*360/5:ii];
    node at (n2.corner i) [dot, label=90+i*360/5:jj];
    node at (n3.corner i) [dot, label=90+i*360/5:kk];
}
%%
foreach j [count=i from 0] in {1,...,5}
{
pgfmathsetmacro{k}{int(1+Mod(i+1,5))}
pgfmathsetmacro{l}{int(1+Mod(i+3,5))}
pgfmathsetmacro{m}{int(1+Mod(i+2,5))}
draw   (n1.corner j) -- (n3.corner j) 
        (n1.corner j) -- (n2.corner k)
        (n2.corner j) -- (n3.corner l)
        (n3.corner j) -- (n3.corner l);
}

end{tikzpicture}
end{document}

Edit:
in the first version of answer was direction the labeling of nodes in opposite direction as is shown in OP images. Now this is corrected with replacing original loop
foreach i [count=j from 6,
             count=k from 11] in {1,...,5}
{
    node at (n1.corner i) [dot, label=90+i*360/5:i];
    node at (n2.corner i) [dot, label=90+i*360/5:j];
    node at (n3.corner i) [dot, label=90+i*360/5:k];
}

with code which is now in above MWE.

TobiBS · Answer

A simple approach for you to start with, it defines a node style mynodes that can be used later. Then you can draw nodes at various locations, e.g. in a polar coordinate system, where the first value is the angle and the second the distance. Then in the end you can draw from any node to any node.
Here is my start for you, but as I didn't find a systematic in the edges, you an probably finish it for yourself:
documentclass[tikz,border=5mm]{standalone}

begin{document}
tikzset{mynodes/.style={inner sep=2pt,fill=black,circle}}
begin{tikzpicture}[scale=2]
    node[mynodes](N1) at (90:3){};
    node[mynodes](N2) at (18:3){};
    node[mynodes](N3) at (-54:3){};
    node[mynodes](N4) at (-126:3){};
    node[mynodes](N5) at (-198:3){};
    
    node[mynodes](N6) at (90:2){};
    node[mynodes](N7) at (18:2){};
    node[mynodes](N8) at (-54:2){};
    node[mynodes](N9) at (-126:2){};
    node[mynodes](N10) at (-198:2){};
    
    node[mynodes](N11) at (90:1){};
    node[mynodes](N12) at (18:1){};
    node[mynodes](N13) at (-54:1){};
    node[mynodes](N14) at (-126:1){};
    node[mynodes](N15) at (-198:1){};
    
    draw (N1) -- (N2) -- (N3) -- (N4) -- (N5) -- (N1);

draw (N1) -- (N10);
    draw (N2) -- (N6); 
    draw (N3) -- (N7); 
    draw (N4) -- (N8);
    draw (N5) -- (N9);
    
    draw (N4) -- (N9) -- (N14) -- (N12) -- (N7) -- (N2);
    draw (N3) -- (N8) -- (N13) -- (N15) -- (N10) -- (N5);
    
    draw (N1) -- (N6) -- (N11) -- (N9);
    
end{tikzpicture}
end{document}

Complications could be introduced by using pgfforeach to define the cyclic nodes, but I avoided that as you mentioned, you are a beginner. For less code this would be useful however.

Nguyen Van Justonly Chi · Answer

For compare purpose.
Compile with Ahihi đồ ngốc.(please don't fix it)
or
http://asymptote.ualberta.ca/
size(7cm);
pair[] P,Q,T;
for (int i=0; i<5;++i){
  P.push(dir(90-i*72));
  Q.push(2/3*dir(90-i*72));
  T.push(1/3*dir(90-i*72));
 }
P.cyclic=true;
T.cyclic=true;
for (int i=0; i<P.length;++i){ 
  label(scale(0.6)*Label("$"+(string) (i+1) +"$"),P[i],dir(degrees(P[i])));
  label(scale(0.6)*Label("$"+(string) (i+6) +"$"),Q[i],dir(degrees(Q[i])+90));
  label(scale(0.6)*Label("$"+(string) (i+11) +"$"),T[i],dir(degrees(T[i])+90));
  draw(P[i]--T[i]);
  draw(P[i+1]--Q[i]);
  draw(Q[i]--T[i+2]);
}
draw(T[0]--T[2]--T[4]--T[1]--T[3]--cycle);
path pentagon=operator --(... P)--cycle;
draw(pentagon);
dot(P);
dot(Q);
dot(T);

I need help with latex tiKz code for drawing the graph

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