# Infinite graphs

I am currently working on a specific class of graphs and I have to enumerate all its forbidden subgraphs. For this, I have to draw several infinite graphs, as shown below.

I know how to draw basic graphs, but I'd like to find instructions or a description on how to draw the like of the graphs above. Any suggestions?

To draw basic graphs, here's what I use:

\documentclass[12pt]{report}
\usepackage{tkz-graph}
\usepackage{amsmath}
\usepackage{tikz}

\begin{document}

\begin{figure}[h]
\centering
\begin{tikzpicture}
\SetGraphUnit{1}
\GraphInit[vstyle=Welsh]
\begin{scope}[rotate=45]CEAB
\Vertices[Lpos=45]{circle}{c,b,d,e}
\end{scope}
\NOEA[Lpos=90,unit=0.728](b){a}
\Edges(e,b,d,e,c,b,a,c)
\end{tikzpicture}
\begin{tikzpicture}
\SetGraphUnit{1}
\GraphInit[vstyle=Welsh]
\begin{scope}[rotate=45]CEAB
\Vertices[Lpos=45]{circle}{c,b,d,e}
\end{scope}
\NOEA[Lpos=90,unit=0.728](b){a}
\Edges(e,b,d,e,c,b,a,c)
\end{tikzpicture}
{\footnotesize $n=5$}

\caption{Two undirected graphs}
\label{grph:01}
\centering
\end{figure}

\end{document}


I was able to do it! Here's my code:

\begin{figure}[H]
\centering
\begin{subfigure}{0.3\textwidth}
\begin{tikzpicture}
\SetGraphUnit{1.5}
\SetVertexSimple
\tikzset{VertexStyle/.style = { shape = circle,
fill = black,
inner sep = 0pt,
outer sep = 0pt,
minimum size = 6pt,
draw}}

\Vertices{circle}{a,b,c,d}
\Edges(a,b,c)\Edge(b)(d)
\end{tikzpicture}
\centering
\caption{$K_{1,3}$ \textit{(claw)}}
\end{subfigure}
\begin{subfigure}{0.2\textwidth}
\begin{tikzpicture}
\SetGraphUnit{1.5}
\SetVertexSimple
\tikzset{VertexStyle/.style = { shape = circle,
fill = black,
inner sep = 0pt,
outer sep = 0pt,
minimum size = 6pt,
draw}}
\Vertices{circle}{1,2,3,4,5,6,7,8,9}
\Edges(1,2,3,4,5,6,7,8,9)
\node [rotate=70] at ($(1)!.45!(9)$) {\ldots};

\end{tikzpicture}
\centering
\caption{$C_{k}(k\geq 4)$}
\end{subfigure}

\begin{subfigure}{0.3\textwidth}
\begin{tikzpicture}
\SetGraphUnit{0.7}
\SetVertexSimple
\tikzset{VertexStyle/.style = { shape = circle,
fill = black,
inner sep = 0pt,
outer sep = 0pt,
minimum size = 6pt,
draw}}
%\draw[help lines] (0,0) grid (5,5);
\Vertices[dir=\SOEA]{line}{3,4,6}
\Vertices[dir=\SOWE]{line}{3,5,7}
\Vertices[dir=\NO]{line}{3,2,1}

\Edges(1,2,3,4,6)
\Edges(3,5,7)

\end{tikzpicture}
\centering
\caption{\textit{bipartite claw}}
\end{subfigure}
\begin{subfigure}{0.3\textwidth}
\begin{tikzpicture}
\SetGraphUnit{0.7}
\SetVertexSimple
\tikzset{VertexStyle/.style = { shape = circle,
fill = black,
inner sep = 0pt,
outer sep = 0pt,
minimum size = 6pt,
draw}}
\Vertices[dir=\NO]{line}{2,1}

\Vertices[dir=\SOWE]{line}{2,3,5}
\Vertices[dir=\SOEA]{line}{2,4,6}
\node[shape = circle,fill = black,inner sep = -2pt,outer sep = -4pt,minimum size = 6pt,draw](7) [right of=3,node distance=0.3cm]{};
\node[shape = circle,fill = black,inner sep = -2pt,outer sep = -4pt,minimum size = 6pt,draw](8) [right of=7,node distance=0.3cm]{};
\Edges(1,2,3,5)
\Edges(2,4,6)
\Edges(3,7,8)
\node at ($(8)!.55!(4)$) {\ldots};
\end{tikzpicture}
\centering
\caption{\textit{n-net }($k\geq 2$)}
\end{subfigure}
\begin{subfigure}{0.3\textwidth}
\begin{tikzpicture}
\SetGraphUnit{1}
\SetVertexSimple
\tikzset{VertexStyle/.style = { shape = circle,
fill = black,
inner sep = 0pt,
outer sep = 0pt,
minimum size = 6pt,
draw}}

\Vertices[dir=\SOWE]{line}{1,2,4}
\Vertices[dir=\SOEA]{line}{1,3,8}
\node[shape = circle,fill = black,inner sep = -2pt,outer sep = -4pt,minimum size = 6pt,draw](5) [right of=4,node distance=0.6cm]{};
\node[shape = circle,fill = black,inner sep = -2pt,outer sep = -4pt,minimum size = 6pt,draw](6) [right of=5,node distance=0.6cm]{};
\node[shape = circle,fill = black,inner sep = -2pt,outer sep = -4pt,minimum size = 6pt,draw](7) [right of=6,node distance=0.6cm]{};
\Edges(1,2,4)
\Edges(1,3,8)
\Edges(3,2)
\Edges(4,5,6,7)
\Edges(2,5)
\Edges(2,6)
\Edges(2,7)
\Edges(3,5)
\Edges(3,6)
\Edges(3,7)
\node at ($(7)!.55!(8)$) {\ldots};
\end{tikzpicture}
\centering
\caption{\textit{n-tent }($k\geq 3$)}
\end{subfigure}

\caption{Caption}
\centering
\label{grph:forbid_indiff}
\end{figure}


This gives the following graphs:

I'll be happy to receive suggestions to improve this.