The Correspondence between Zero-divisor Graphs with 6 Vertices and Their Semigroups
نویسندگان
چکیده
The idea of associating a graph with the zero-divisors of a commutative ring was originated by Beck. The problems concerning zero-divisor graphs have been studied extensively in the past 10 years. DeMeyer and DeMeyer presented some properties for the correspondence between zero-divisor graphs and their semigroups. It is very important to have adequate examples before the complete resolution of this difficult problem. However, the computing cost is enormous even when there are only 6 vertices. We present a program with elaborate optimization and pruning that can solve the correspondence between zero-divisor graphs with 6 vertices and their semigroups rapidly.
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