vertex of the base-graph); Squares: added vertices (base-location : edge of the base-graph). (a) Trap-colouring. Green: computation qubits; White/black: trap qubits; Red: dummy qubits. Client chooses the trap-colouring, prepares each qubit individually and sends them one by one for the server to entangle according to the generic construction. (b) After entangling, the breaking operation defined by the dummy qubits will reduce the graph in (a) to the computation graph and for each vertex a corresponding trap/tag qubits.[]{data-label="figure3"}](figure3.jpg){width="1\columnwidth"}

The flow, Past of qubit $i$ and Influence-past of qubit $i$ can all be extended to the Dotted-Triple-Graph construction, with the result that each qubit still depends on a constant number of previous measurements (see [@KW15]).

For completeness we give the verification protocol from [@KW15] that we use:

We assume that a standard labeling of the vertices of the dotted triple-graph $DT(G)$ is known to both the client and the server. The number of qubits is at most $3N(3c+1)$ where $c$ is the maximum degree of the base graph $G$.\
$\bullet$ **Client’s resources**\
– Client is given a base graph $G$. The corresponding dotted graph state $\ket{D(G)}$ is generated by graph $D(G)$ that is obtained from $G$ by replacing every edge with a 