The exponent of the Weyl group of given type. This is the least common multiple of the orders of the elements of the group. In a comment to [4], see also [5], it is asked whether this is the same as the least common multiple of the degrees of the Weyl group.

The order of rowmotion on the root poset of a finite Cartan type.

The order of rowmotion on the set of order ideals of a poset.

The number of vertices of odd degree in a graph.

The least common multiple of the parts of the partition.

The decimal representation of a binary word with a leading 1. This statistic is obtained by prepending $1$ to the binary word and interpreting it as a number in binary.

The energy of a graph, if it is integral. The energy of a graph is the sum of the absolute values of its eigenvalues. This statistic is only defined for graphs with integral energy. It is known, that the energy is never an odd integer [2]. In fact, it is never the square root of an odd integer [3]. The energy of a graph is the sum of the energies of the connected components of a graph. The energy of the complete graph $K_n$ equals $2n-2$. For this reason, we do not define the energy of the empty graph.

The minimal number of edges to add or remove to make a graph regular.

The minimal number of edges to add or remove to make a graph vertex transitive. A graph is vertex transitive if for any two edges there is an automorphism that maps one vertex to the other.

The villainy of a graph. The villainy of a permutation of a proper coloring $c$ of a graph is the minimal Hamming distance between $c$ and a proper coloring. The villainy of a graph is the maximal villainy of a permutation of a proper coloring.