\documentclass[tikz]{standalone}

\usetikzlibrary{decorations.pathreplacing,decorations.markings}
\usetikzlibrary{patterns}

\standaloneconfig{margin=12pt}

\begin{document}

\begin{tikzpicture}

%diagonals + diagonal labels
\draw[gray,thick,dashed] (0,1) to node[midway,right,yshift=2pt,xshift=-2pt]{ $a$} (1,0);
\draw[gray,thick,dashed] (1,1) to node[midway,right,yshift=2pt,xshift=-2pt]{ $1$} (2,0);
\draw[gray,thick,dashed] (1,2) to node[midway,right,yshift=2pt,xshift=-2pt]{$1$}  (2,1);
\draw[gray,thick,dashed] (2,2) to node[midway,right,yshift=2pt,xshift=-2pt]{$b$}  (3,1);


%snake graph outline
\draw[thick] (0,0) to (1,0) to node[midway,right,xshift=-1pt,scale=0.75]{$b$}  (1,1) to node[midway,above,yshift=-1pt,scale=0.75]{$1$} (0,1) to (0,0);
\draw[thick] (1,0) to node[midway,below,yshift=1pt,scale=0.75]{$a$}  (2,0) to node[midway,right,xshift=-1pt,scale=0.75]{$1$}  (2,1) to node[midway,above,yshift=-2pt,scale=0.75]{$\mu$} (1,1);
\draw[thick] (1,1) to (1,2) to node[midway,above,yshift=-1pt,scale=0.75]{$b$}  (2,2);
\draw[thick] (2,1) to (3,1) to (3,2) to (2,2) to node[midway,right,xshift=-1pt,scale=0.75]{$a$}  (2,1);


\end{tikzpicture}

\end{document}