The metric dimension of a graph. This is the length of the shortest vector of vertices, such that every vertex is uniquely determined by the vector of distances from these vertices.

The largest eigenvalue of a graph if it is integral. If a graph is $d$-regular, then its largest eigenvalue equals $d$. One can show that the largest eigenvalue always lies between the average degree and the maximal degree. This statistic is undefined if the largest eigenvalue of the graph is not integral.

The number of atoms of a lattice. An element of a lattice is an '''atom''' if it covers the least element.

The jump number of the poset. A jump in a linear extension $e_1, \dots, e_n$ of a poset $P$ is a pair $(e_i, e_{i+1})$ so that $e_{i+1}$ does not cover $e_i$ in $P$. The jump number of a poset is the minimal number of jumps in linear extensions of a poset.

The maximal number of elements covered by an element in a poset.

The maximal number of elements covering an element of a poset.

The number of maximal chains of minimal length in a poset.

The size of the largest ordinal summand in the poset. The ordinal sum of two posets $P$ and $Q$ is the poset having elements $(p,0)$ and $(q,1)$ for $p\in P$ and $q\in Q$, and relations $(a,0) < (b,0)$ if $a < b$ in $P$, $(a,1) < (b,1)$ if $a < b$ in $Q$, and $(a,0) < (b,1)$. This statistic is the maximal cardinality of a summand in the longest ordinal decomposition of a poset.