\documentclass[tikz]{standalone}

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

\begin{document}

\begin{tikzpicture}

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


%snake graph outline
\draw[thick] (0,1) to node[midway,left,scale=0.75,xshift=1pt]{$U_{k+1} x_1$} (0,2) to node[midway,above,scale=0.75,xshift=-2pt]{$x_2$}  (1,2) to node[midway,right,scale=0.75,xshift=-2pt, yshift = -8pt]{$x_a$}  (1,1) to node[midway,below,scale=0.75,xshift=1pt]{$U_k x_1$} (0,1);
\draw[thick] (2,1) to node[midway,left,scale=0.75,yshift=8pt]{$U_k x_1$}  (2,2) to node[midway,above,scale=0.75,xshift=-1pt]{$x_a$}  (3,2) to node[midway,right,scale=0.75,xshift=-1pt]{$x_2$} (3,1)  to node[midway,below,scale=0.75,yshift=-1pt]{$U_{k+1} x_1$}  (2,1);



\end{tikzpicture}

\end{document}