The packing number of a graph. This is the size of a largest subset of vertices of a graph, such that any two distinct vertices in the subset have disjoint closed neighbourhoods, or, equivalently, have distance greater than two.

The number of connected components of a graph.

The Euler characteristic of a graph. The '''Euler characteristic''' $\chi$ of a topological space is the alternating sum of the dimensions of the homology groups $$\chi(X) = \sum_{k \geq 0} (-1)^k \dim H_k(X).$$ For a finite simplicial complex, this is equal to the alternating sum $ \sum_{k\geq 0} (-1)^k f_k$ where $f_k$ the number of $k$-dimensional simplices. A (simple) graph is a simplicial complex of dimension at most one; its vertices are the 0-simplices and its edges are the 1-simplices. For a connected graph, the Euler characteristic is equal to $1 - g$ where $g$ is the cyclomatic number.

The number of connected components of the complement of a graph. The complement of a graph is the graph on the same vertex set with complementary edges.

The vector space dimension of the first extension group between the socle of the regular module and the Jacobson radical of the corresponding Nakayama algebra.