Semigroup Invariants of Graphs with Respect to Their Approximability

This paper continues the consideration of the notion of approximability of a semigroup with respect to a predicate. This problem related to isomorphism of semigroups can be reduced to the problem of computing graph invariants. The paper investigates the problem of computing invariants in the case of representation of a finite graph by a adjacency matrix, and selects the invariants that most effectively distinguish non-isomorphic semigroups. A theorem has been proved stating that the diameter of a graph, the number of edges and the determinant of the adjacency matrix are not semigroup invariants for semigroups of a given order n with respect to the composition mapping. #COMESYSO1120.