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 SM ISO690:2012AFKHAMI, Mojgan, KHASHYARMANESH, Kazem, SAKHDARI, Seyed Mohammad. Annihilator graph of a commutative semigroup whose zero-divisor graph is a refinement of a star graph. In: Quasigroups and Related Systems, 2021, vol. 29, nr. 2(46), pp. 157-170. ISSN 1561-2848. |
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 Quasigroups and Related Systems |
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| Volumul 29, Numărul 2(46) / 2021 / ISSN 1561-2848 | |
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| Pag. 157-170 | |
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Suppose that G is a refinement of a star graph with center c and G is the subgraph of G induced on the vertices V (G) n fx 2 V (G) j x = c or x is an end vertex adjacent to cg. Let S be a commutative semigroup with zero and Г(S) be the zero-divisor graph of S. In this paper, we determine the structure of the annihilator graph of S by using the zero-divisor graph Г(S), which is a refinement of a star graph with center c, and Г(S) has at least two components or Г(S) is isomorphic to a cycle graph or a path. |
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