
COMMENTS

An invariant on graphs is a function that takes the same values on isomorphic graphs.
A 4invariant f is an invariant such that for any graph G and any pair of vertices A,B connected by an edge in G,
f(G)  f(r(G,A,B)) = f(t(G,A,B))  f(r(t(G,A,B),A,B)),
where:
r(G,A,B)=r(G,B,A) is a graph obtained from G by removal of edge (A,B);
t(G,A,B) is a graph H obtained from G by modifying the neighborhood of vertex A: N_H(A) is the symmetric difference of N_G(A) and N_G(B). (Note that t(G,A,B) and t(G,B,A) may differ.)
The 4invariants on graphs with n vertices form a vector space, whose dimension is given by this sequence.
Similar 4invariants can be defined on graphs with each vertex A having a label l(A) from the set {0,1}. In this case, the definition of r(G,A,B) and t(G,A,B) is the same when l(B)=0, but if l(B)=1 then in t(G,A,B) the value of l(A) is inverted and the edge (A,B) is removed, while in r(t(G,A,B),A,B) this edge is added back. The dimensions of the vector space of such 4invariants on graphs with n<=5 vertices are 2,5,11,26,58. These values match A026787 but do they really represent this sequence?
