\documentclass[tikz,border=5pt]{standalone}
\usepackage[utf8]{inputenc}
\usepackage{amsmath,amsthm,amssymb}
\usepackage{tikz}
\usetikzlibrary{calc}
\usetikzlibrary{decorations.shapes, shapes.geometric}
\begin{document}
\begin{tikzpicture}[scale=0.78]
\tikzstyle{vertex_red}=[draw, shape=regular polygon, regular polygon sides=3, fill=red, minimum size=12pt, inner sep=0]
\tikzstyle{vertex_blue}=[draw, shape=rectangle, fill=blue, minimum size=8pt, inner sep=0]
\tikzstyle{vertex_green}=[draw, shape=diamond, fill=green, minimum size=11pt, inner sep=0]
\tikzstyle{vertex_yellow}=[draw, shape=star, fill=yellow, minimum size=11pt, inner sep=0]
\footnotesize
\node[vertex_red] (v11) at (0,5) [label={[xshift=0pt, yshift=-1pt] $v_{1,1}$}] {};
\node[vertex_red] (v12) at (1,5) [label={[xshift=0pt, yshift=-1pt] $v_{1,2}$}] {};
\node[vertex_red] (v13) at (2,5) [label={[xshift=0pt, yshift=-1pt] $v_{1,3}$}] {};
\node[vertex_blue] (v21) at (0,4) [label={[xshift=-14pt, yshift=-10pt] $v_{2,1}$}] {};
\node[vertex_blue] (v31) at (0,3) [label={[xshift=-14pt, yshift=-10pt] $v_{3,1}$}] {};
\node[vertex_green] (v41) at (0,2) [label={[xshift=-14pt, yshift=-10pt] $v_{4,1}$}] {};
\node[vertex_green] (v51) at (0,1) [label={[xshift=-14pt, yshift=-10pt] $v_{5,1}$}] {};
\node[vertex_yellow] (v61) at (0,0) [label=below:$v_{6,1}$] {};
\node[vertex_yellow] (v62) at (1,0) [label=below:$v_{6,2}$] {};
\draw[very thick] (v11) -- (v12) -- (v13);
\draw[very thick] (v61) -- (v62);
\draw[very thick] (v11) -- (v21) -- (v31) -- (v41) -- (v51) -- (v61);
\draw[very thick] (v12) -- (v62);
\draw[very thick] (v13) -- (v62);
\begin{scope}[shift={(3.5,0)}]
\node[vertex_red] (v11) at (0,5) [label={[xshift=0pt, yshift=-1pt] $v_{1,1}$}] {};
\node[vertex_red] (v12) at (1,5) [label={[xshift=0pt, yshift=-1pt] $v_{1,2}$}] {};
\node[vertex_red] (v13) at (2,5) [label={[xshift=0pt, yshift=-1pt] $v_{1,3}$}] {};
\node[vertex_blue] (v21) at (0,4) [label={[xshift=-14pt, yshift=-10pt] $v_{2,1}$}] {};
\node[vertex_blue] (v31) at (0,3) [label={[xshift=-14pt, yshift=-10pt] $v_{3,1}$}] {};
\node[vertex_green] (v41) at (0,2) [label={[xshift=-14pt, yshift=-10pt] $v_{4,1}$}] {};
\node[vertex_green] (v51) at (0,1) [label={[xshift=-14pt, yshift=-10pt] $v_{5,1}$}] {};
\node[vertex_yellow] (v61) at (0,0) [label=below:$v_{6,1}$] {};
\node[vertex_yellow] (v62) at (1,0) [label=below:$v_{6,2}$] {};
\node[vertex_yellow] (v63) at (2,0) [label=below:$v_{6,3}$] {};
\draw[very thick] (v11) -- (v12) -- (v13);
\draw[very thick] (v61) -- (v62) -- (v63);
\draw[very thick] (v11) -- (v21) -- (v31) -- (v41) -- (v51) -- (v61);
\draw[very thick] (v12) -- (v62);
\draw[very thick] (v13) -- (v63);
\end{scope}
\begin{scope}[shift={(7,0)}]
\node[vertex_red] (v11) at (0,5) [label={[xshift=0pt, yshift=-1pt] $v_{1,1}$}] {};
\node[vertex_red] (v12) at (1,5) [label={[xshift=0pt, yshift=-1pt] $v_{1,2}$}] {};
\node[vertex_red] (v13) at (2,5) [label={[xshift=0pt, yshift=-1pt] $v_{1,3}$}] {};
\node[vertex_blue] (v21) at (0,4) [label={[xshift=-14pt, yshift=-10pt] $v_{2,1}$}] {};
\node[vertex_blue] (v22) at (1,4) [label={[xshift=13pt, yshift=-10pt] $v_{2,2}$}] {};
\node[vertex_blue] (v31) at (0,3) [label={[xshift=-14pt, yshift=-10pt] $v_{3,1}$}] {};
\node[vertex_green] (v41) at (0,2) [label={[xshift=-14pt, yshift=-10pt] $v_{4,1}$}] {};
\node[vertex_green] (v51) at (0,1) [label={[xshift=-14pt, yshift=-10pt] $v_{5,1}$}] {};
\node[vertex_yellow] (v61) at (0,0) [label=below:$v_{6,1}$] {};
\node[vertex_yellow] (v62) at (1,0) [label=below:$v_{6,2}$] {};
\node[vertex_yellow] (v63) at (2,0) [label=below:$v_{6,3}$] {};
\draw[very thick] (v11) -- (v12) -- (v13);
\draw[very thick] (v61) -- (v62) -- (v63);
\draw[very thick] (v11) -- (v21) -- (v31) -- (v41) -- (v51) -- (v61);
\draw[very thick] (v12) -- (v22) -- (v62);
\draw[very thick] (v13) -- (v63);
\end{scope}
\begin{scope}[shift={(10.5,0)}]
\node[vertex_red] (v11) at (0,5) [label={[xshift=0pt, yshift=-1pt] $v_{1,1}$}] {};
\node[vertex_red] (v12) at (1,5) [label={[xshift=0pt, yshift=-1pt] $v_{1,2}$}] {};
\node[vertex_red] (v13) at (2,5) [label={[xshift=0pt, yshift=-1pt] $v_{1,3}$}] {};
\node[vertex_blue] (v21) at (0,4) [label={[xshift=-14pt, yshift=-10pt] $v_{2,1}$}] {};
\node[vertex_blue] (v22) at (1,4) [label={[xshift=13pt, yshift=-10pt] $v_{2,2}$}] {};
\node[vertex_blue] (v31) at (0,3) [label={[xshift=-14pt, yshift=-10pt] $v_{3,1}$}] {};
\node[vertex_blue] (v32) at (1,3) [label={[xshift=13pt, yshift=-10pt] $v_{3,2}$}] {};
\node[vertex_green] (v41) at (0,2) [label={[xshift=-14pt, yshift=-10pt] $v_{4,1}$}] {};
\node[vertex_green] (v51) at (0,1) [label={[xshift=-14pt, yshift=-10pt] $v_{5,1}$}] {};
\node[vertex_yellow] (v61) at (0,0) [label=below:$v_{6,1}$] {};
\node[vertex_yellow] (v62) at (1,0) [label=below:$v_{6,2}$] {};
\node[vertex_yellow] (v63) at (2,0) [label=below:$v_{6,3}$] {};
\draw[very thick] (v11) -- (v12) -- (v13);
\draw[very thick] (v61) -- (v62) -- (v63);
\draw[very thick] (v11) -- (v21) -- (v31) -- (v41) -- (v51) -- (v61);
\draw[very thick] (v12) -- (v22) -- (v32) -- (v62);
\draw[very thick] (v13) -- (v63);
\end{scope}
\begin{scope}[shift={(14,0)}]
\node[vertex_red] (v11) at (0,5) [label={[xshift=0pt, yshift=-1pt] $v_{1,1}$}] {};
\node[vertex_red] (v12) at (1,5) [label={[xshift=0pt, yshift=-1pt] $v_{1,2}$}] {};
\node[vertex_red] (v13) at (2,5) [label={[xshift=0pt, yshift=-1pt] $v_{1,3}$}] {};
\node[vertex_blue] (v21) at (0,4) [label={[xshift=-14pt, yshift=-10pt] $v_{2,1}$}] {};
\node[vertex_blue] (v22) at (1,4) [label={[xshift=13pt, yshift=-10pt] $v_{2,2}$}] {};
\node[vertex_blue] (v31) at (0,3) [label={[xshift=-14pt, yshift=-10pt] $v_{3,1}$}] {};
\node[vertex_blue] (v32) at (1,3) [label={[xshift=13pt, yshift=-10pt] $v_{3,2}$}] {};
\node[vertex_green] (v41) at (0,2) [label={[xshift=-14pt, yshift=-10pt] $v_{4,1}$}] {};
\node[vertex_green] (v42) at (1,2) [label={[xshift=13pt, yshift=-10pt] $v_{4,2}$}] {};
\node[vertex_green] (v51) at (0,1) [label={[xshift=-14pt, yshift=-10pt] $v_{5,1}$}] {};
\node[vertex_yellow] (v61) at (0,0) [label=below:$v_{6,1}$] {};
\node[vertex_yellow] (v62) at (1,0) [label=below:$v_{6,2}$] {};
\node[vertex_yellow] (v63) at (2,0) [label=below:$v_{6,3}$] {};
\draw[very thick] (v11) -- (v12) -- (v13);
\draw[very thick] (v61) -- (v62) -- (v63);
\draw[very thick] (v11) -- (v21) -- (v31) -- (v41) -- (v51) -- (v61);
\draw[very thick] (v12) -- (v22) -- (v32) -- (v42) -- (v62);
\draw[very thick] (v13) -- (v63);
\end{scope}
\begin{scope}[shift={(17.5,0)}]
\node[vertex_red] (v11) at (0,5) [label={[xshift=0pt, yshift=-1pt] $v_{1,1}$}] {};
\node[vertex_red] (v12) at (1,5) [label={[xshift=0pt, yshift=-1pt] $v_{1,2}$}] {};
\node[vertex_red] (v13) at (2,5) [label={[xshift=0pt, yshift=-1pt] $v_{1,3}$}] {};
\node[vertex_blue] (v21) at (0,4) [label={[xshift=-14pt, yshift=-10pt] $v_{2,1}$}] {};
\node[vertex_blue] (v22) at (1,4) [label={[xshift=13pt, yshift=-10pt] $v_{2,2}$}] {};
\node[vertex_blue] (v31) at (0,3) [label={[xshift=-14pt, yshift=-10pt] $v_{3,1}$}] {};
\node[vertex_blue] (v32) at (1,3) [label={[xshift=13pt, yshift=-10pt] $v_{3,2}$}] {};
\node[vertex_green] (v41) at (0,2) [label={[xshift=-14pt, yshift=-10pt] $v_{4,1}$}] {};
\node[vertex_green] (v42) at (1,2) [label={[xshift=13pt, yshift=-10pt] $v_{4,2}$}] {};
\node[vertex_green] (v51) at (0,1) [label={[xshift=-14pt, yshift=-10pt] $v_{5,1}$}] {};
\node[vertex_green] (v52) at (1,1) [label={[xshift=13pt, yshift=-10pt] $v_{5,2}$}] {};
\node[vertex_yellow] (v61) at (0,0) [label=below:$v_{6,1}$] {};
\node[vertex_yellow] (v62) at (1,0) [label=below:$v_{6,2}$] {};
\node[vertex_yellow] (v63) at (2,0) [label=below:$v_{6,3}$] {};
\draw[very thick] (v11) -- (v12) -- (v13);
\draw[very thick] (v61) -- (v62) -- (v63);
\draw[very thick] (v11) -- (v21) -- (v31) -- (v41) -- (v51) -- (v61);
\draw[very thick] (v12) -- (v22) -- (v32) -- (v42) -- (v52) -- (v62);
\draw[very thick] (v13) -- (v63);
\end{scope}
\end{tikzpicture}
\end{document}