Abstract

For a refinement of a finite or an infinite star graph G with center c, let G_c* be the subgraph of G induced on the vertices of G that not include the center c or end vertices adjacent to c. In this paper, we study properties of commutative nilpotent semigroups whose zero-divisor graph is isomorphic to G. We completely determine the structure of commutative nilpotent semigroups S such that the induced graph of the zero-divisor graph of S is a star graph with two edges, and we prove that the semigroups S is unique under isomorphism. We also give counting formulas for the number of all such semigroups in the finite cases in the third part. The result of our study will contribute to the semigroup theory in computer code areas.

Paper Details