Where can I find document of this?

[heroboy]

I know https://cspsat.gitlab.io/sugar/
But what is "graph-active-vertices-connected"?

[semiexp]

I'm afraid I have not written any document...

Syntax for graph-active-vertices-connected is as follows:

(graph-active-vertices-connected <num-vertices> <num-edges> <v[0]> ... <v[n-1]> <p[0]> <q[0]> <p[1]> <q[1]> ... <p[m-1]> <q[m-1]>)

Here, n is num-vertices and m is num-edges. <v[i]> is boolean expressions, and <p[i]> and <q[i]> are integer literals (complex expressions are not allowed).

The semantics for this operator is, simply put, "in a fixed graph, selected vertices are connected".
More precisely, suppose we have an undirected graph $G$ with $n$ vertices and $m$ edges.
Vertices are numbered by $0$, $1$, $\dots$, $n-1$ and the $i$-th edge connects vertices p[i] and q[i].
v[i] is a boolean expression representing whether the vertex $i$ is selected.
Then all selected vertices (those whose corresponding v[i] is true) should be connected, that is, for any selected two vertices $u$ and $v$, there must be a path connecting $u$ and $v$ such that vertices on the path are all selected.
In other words, the induced subgraph of $G$ with the selected vertices must be connected (or empty).

[heroboy]

Thank you for your detailed explanation.
I wonder why you add this when original sugar doesn't have this.

[semiexp]

I added this because this will be useful for solving pencil puzzle problems (https://github.com/semiexp/cspuz).