sentence1: the roots of the theory of wordrepresentable graphs are in the study of the celebrated perkins semigroup which has played a central role in semigroup theory since 1960 , particularly as a source of examples and counterexamples .
sentence2: the roots of the theory of word-representable graphs are in the study of the celebrated perkins semigroup in , which has played a central role in semigroup theory since 1960 , particularly as a source of examples and counterexamples .