The weak 2-dynamic chromatic number of a graph. A $k$-weak-dynamic coloring of a graph $G$ is a (non-proper) coloring of $G$ in such a way that each vertex $v$ sees at least $\min\{d(v), k\}$ colors in its neighborhood. The $k$-weak-dynamic number of a graph is the smallest number of colors needed to find an $k$-dynamic coloring. This statistic records the $2$-weak-dynamic number of a graph.

The distinguishing index of a graph. This is the smallest number of colours such that there is a colouring of the edges which is not preserved by any automorphism. If the graph has a connected component which is a single edge, or at least two isolated vertices, this statistic is undefined.

The number of prime labellings of a graph. A prime labelling of a graph is a bijective labelling of the vertices with the numbers $\{1,\dots, |V(G)|\}$ such that adjacent vertices have coprime labels.

The number of doubly irreducible elements of a lattice. An element $d$ of a lattice $L$ is '''doubly irreducible''' if it is both join and meet irreducible. That means, $d$ is neither the least nor the greatest element of $L$ and if $d=x\vee y$ or $d=x\wedge y$, then $d\in\{x,y\}$ for all $x,y\in L$. In a finite lattice, the doubly irreducible elements are those which cover and are covered by a unique element.