Graph
Vertex list
$V = ( g, r, w, b, y )$
Adjacency matrix
$ A = \begin{bmatrix} 0 & 1 & 1 & 1 & 1 \\ 1 & 0 & 0 & 0 & 1 \\ 1 & 0 & 0 & 0 & 0 \\ 1 & 0 & 0 & 0 & 1 \\ 1 & 1 & 0 & 1 & 0 \\ \end{bmatrix} $
Symmetry
$A = A^\intercal$
String
$A = \begin{bmatrix} 0 & 1 & 1 & 1 & 1 \\ \textcolor{#0072c3}{1} & 0 & 0 & 0 & 1 \\ \textcolor{#0072c3}{1} & \textcolor{#0072c3}{0} & 0 & 0 & 0 \\ \textcolor{#0072c3}{1} & \textcolor{#0072c3}{0} & \textcolor{#0072c3}{0} & 0 & 1 \\ \textcolor{#0072c3}{1} & \textcolor{#0072c3}{1} & \textcolor{#0072c3}{0} & \textcolor{#0072c3}{1} & 0 \\ \end{bmatrix}$
$s = \textcolor{#0072c3}{1101001101}$