The stock of Farmington-based Darwin Professional Underwriters Inc. will now be traded on the main floor of the New York Stock Exchange, after spending most of the last year being traded on the Arca, an all-electronic-exchange owned by the NYSE. It became the first company anywhere to make that transition onto The Big Board from Arca. Darwin, whose DR ticker symbol remains unchanged, held its initial public offering on May 19. Senior executives and directors of the company were scheduled to ring the opening bell on Wall St. this morning.