Need help with tex code for drawing the two graphs in latex

Question

I would like to draw these two graphs in LaTeX. I am new and just learning the code for graphs.

Each drawing should take up about 5cm sq area.

Any help!!

Answer 1

Since I don't know how to use the graphs library of TikZ, here is an example of what you can do simply with coordinates:

\documentclass{standalone}

\usepackage{tikz}
    \usetikzlibrary{calc}
    
\begin{document}
    
    \begin{tikzpicture}
    
        \newcommand{\biglength}{5}
        \newcommand{\smalllength}{2}
    
        \draw (0, 0)                  coordinate (a) node[above] {$a$}
            -- ++ (0:\smalllength)    coordinate (b) node[above] {$b$}
            -- ++ (-60:\biglength)    coordinate (d) node[below right] {$d$}
            -- ++ (-120:\smalllength) coordinate (e) node[below right] {$e$}
            -- ++ (-180:\biglength)   coordinate (g) node[below left] {$g$}
            -- ++ (120:\smalllength)  coordinate (h) node[below left] {$h$}
            -- cycle;
            
        \draw (a) 
            -- (b)
            -- ++ (-120:\smalllength) coordinate (c) node[right] {$c$} 
            -- cycle; 
            
        \draw (d)
            -- (e)
            -- ++ (120:\smalllength) coordinate (f) node[below left] {$f$}
            -- cycle;
            
        \draw (g)
            -- (h)
            -- ++ (0:\smalllength) coordinate (i) node[below right] {$i$}
            -- cycle;

        \coordinate (center) at ($(c) + (0, {-(\biglength - \smalllength)*sqrt(3)/3})$);
        
        \coordinate (j) at ($(center) + (90:{\smalllength*sqrt(3)/3})$);
        \coordinate (k) at ($(center) + (-30:{\smalllength*sqrt(3)/3})$);
        \coordinate (l) at ($(center) + (-150:{\smalllength*sqrt(3)/3})$);
        \draw (c) -- (j) node[left] {$j$};
        \draw (f) -- (k) node[above right] {$k$};
        \draw (i) -- (l) node[above left] {$l$};

        \draw (j) -- (k) -- (l) -- cycle;

        \foreach \x in {a,b,c,d,e,f,g,h,i,j,k,l}{
            \fill[red] (\x) circle (0.05);
        }

    \end{tikzpicture}
    
    \begin{tikzpicture}
    
        \newcommand{\biglength}{7}
    
        \coordinate (a) at (0, 0);
        \coordinate (b) at (-60:\biglength);
        \coordinate (c) at (-120:\biglength);
        
        \coordinate (d) at ($(a) + (0, {-\biglength*sqrt(3)/4})$);
        \coordinate (e) at ($(b) + (150:{\biglength*sqrt(3)/4})$);
        \coordinate (f) at ($(c) + (30:{\biglength*sqrt(3)/4})$);
        
        \draw (a) -- (e) -- (c) -- (d) -- (b) -- (f) -- cycle;  
        \draw (a) node[above] {$a$} 
            -- (d) node[below] {$d$};
        \draw (b) node[below right] {$b$}
            -- (e) node[above left] {$e$};
        \draw (c) node[below left] {$c$}
            -- (f) node[above right] {$f$}; 
            
        \foreach \x in {a,b,c,d,e,f}{
            \fill[red] (\x) circle (0.05);  
        }
    
    \end{tikzpicture}
    
\end{document}

which yields:

If you want to adapt the size, you can use the scale option of the tikzpicture environment. If you want to further tune the graphs, you can look at TikZ documentation.

Moreover, using the package tkz-euclide with \usepackage{tkz-euclide} it is even possible to replace the line \coordinate (center) at ($(c) + (0, {-(\biglength - \smalllength)*sqrt(3)/3})$); in the definition of the first figure by:

\tkzCircumCenter(c,f,i)
\tkzGetPoint{center}

to be sure of the position of the central part of the graph.

Answer 2

% Edited from --The seven bridges of Königsberg at http://mirror.iopb.res.in/tex-archive/obsolete/macros/latex/contrib/tkz/tkz-graph/doc/tkz-graph-screen.pdf
% Author : Alain Matthes
% Encoding : UTF8
% Engine : PDFLaTeX
\documentclass[]{article}
\usepackage[utf8]{inputenc}
\usepackage{fullpage}
\usepackage{fourier}
\usepackage{tikz}
\usetikzlibrary{arrows,shapes,positioning,calc}
\begin{document}
\begin{center}
\begin{tikzpicture}
\tikzset{VertexStyle/.style = {shape = circle,
                                ball color = orange,
                                text = black,
                                inner sep = 0pt,
                                outer sep = 0pt,
                                minimum size = 8 pt}}
\tikzset{EdgeStyle/.style = {thick,
                                double = orange,
                                double distance = 1pt}}
\tikzset{LabelStyle/.style = {draw,
                                fill = yellow,
                                text = red}}

\node[VertexStyle,label={[label distance=1pt]30:a}](A){};
\node[VertexStyle,right=of A,label={[label distance=1pt]30:b}](B){};
\node[VertexStyle,below=of $(A)!.5!(B)$,label={[label distance=1pt]30:c}](C){};

\node[VertexStyle,below=5cm of A,xshift=-3cm,label={[label distance=1pt]30:h}](H){};
\node[VertexStyle,right=of H,label={[label distance=1pt]30:i}](I){};
\node[VertexStyle,below=of $(H)!.5!(I)$,label={[label distance=1pt]30:g}](G){};

\node[VertexStyle,below=5cm of A,xshift=3cm,label={[label distance=1pt]30:f}](F){};
\node[VertexStyle,right=of F,label={[label distance=1pt]30:d}](D){};
\node[VertexStyle,below=of $(F)!.5!(D)$,label={[label distance=1pt]30:e}](E){};

\node[VertexStyle,below=1.5cm of C,label={[label distance=1pt]30:j}](J){};
\node [below=  of J    ](J1){};
\node [VertexStyle,label={[label distance=1pt]30:l}] at (J1-|A) (L){};
\node [VertexStyle,label={[label distance=1pt]30:k}] at (J1-|B) (K){};


\draw[EdgeStyle](A) to  (B)to (C)to (A);
\draw[EdgeStyle](H) to (I) to(G) to(H) ;
\draw[EdgeStyle](F) to (D) to(E) to(F) ;
\draw[EdgeStyle](J) to (K) to(L) to(J) ;
\draw[EdgeStyle](A) to (H) (G)to(E) (B)to(D) ;
\draw[EdgeStyle](I) to (L) (C)to(J) (K)to(F) ;

\end{tikzpicture}
\end{center}
\end{document}