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In this paper, we consider various graphs, namely: power graph, cyclic graph,enhanced power graph and commuting graph, on a finite semigroup $S$. For anarbitrary pair of these four graphs, we classify finite semigroups such thatthe graphs in this pair are equal. In this connection, for each of the graph wealso give a necessary and sufficient condition on $S$ such that it is complete.The work of this paper generalize the corresponding results obtained forgroups.

Equality of various graphs on finite semigroups