The final chapter of Frank Graham’s dynamic history of the New York Giants is entitled "With One Swipe of His Bat.” For sheer drama and a colossal slice of baseball legend, the core of that chapter cannot be topped--Bobby Thomson’s "shot heard ’round the world,” the three-run homer in the 1951 playoff series that determined that the Giants--not the Dodgers--would win the pennant.              Graham, of course, starts at the beginning, 1883, the year the Giants were born. With characteristic panache, Graham tells us how it was: "This was New York in the elegant eighties and these were the Giants, fashioned in elegance, playing on the Polo Grounds. . . . It was the New York of the brownstone house and the gaslit streets, of the top hat and the hansom cab, of oysters and champagne and perfecto cigars, of [actress] Ada Rehan and Oscar Wilde and the young John L. Sullivan. It also was the New York of the Tenderloin and the Bowery.”              One of fifteen team histories commissioned by G. P. Putnam’s Sons in the 1940s and 1950s, The New York Giants was first published in 1952. Some of the most colorful characters in the game pass through these pages as well as some of baseball’s brightest legends, many of whom appear in the book’s twenty-three photographs.              Hall of Famers Christy Mathewson, Mel Ott, Frankie Frisch, Carl Hubbell, and Bill Terry star among the headliners in the illustrious history of the Giants. Other Hall of Famers include John McGraw, "Beauty” Dave Bancroft, "Iron Man” Joe McGinnity, Leo Durocher, Buck Ewing, Amos Rusie, John Montgomery Ward, and Ross Youngs.              In his foreword, Ray Robinson gives his impression of Frank Graham: "I had been reading Graham’s warm 'conversation pieces’ for some years, first in the New York Sun, then in the Journal-American, but I had no idea how kind and modest he was. The columnist Red Smith, Graham’s good friend, once referred to him as 'a digger for truth, a reporter of facts . . . with an incredibly accurate ear and an implausibly retentive memory.’ To Smith, Graham was the finest sports columnist of his time.”