The 2-limited packing number of a graph. A subset $B$ of the set of vertices of a graph is a $k$-limited packing set if its intersection with the (closed) neighbourhood of any vertex is at most $k$. The $k$-limited packing number is the largest number of vertices in a $k$-limited packing set.

The second largest eigenvalue of a graph if it is integral. This statistic is undefined if the second largest eigenvalue of the graph is not integral. Chapter 4 of [1] provides lots of context.

The number of simple modules with projective dimension at most 1.

The radius of a connected graph. This is the minimum eccentricity of any vertex.

The game chromatic index of a graph. Two players, Alice and Bob, take turns colouring properly any uncolored edge of the graph. Alice begins. If it is not possible for either player to colour a edge, then Bob wins. If the graph is completely colored, Alice wins. The game chromatic index is the smallest number of colours such that Alice has a winning strategy.

The lettericity of a graph. Let $D$ be a digraph on $k$ vertices, possibly with loops and let $w$ be a word of length $n$ whose letters are vertices of $D$. The letter graph corresponding to $D$ and $w$ is the graph with vertex set $\{1,\dots,n\}$ whose edges are the pairs $(i,j)$ with $i < j$ sucht that $(w_i, w_j)$ is a (directed) edge of $D$.

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 projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L.

The number of 2-regular simple modules in the incidence algebra of the lattice.

Number of indecomposable injective modules with projective dimension 2.