Washington Post Co. Chairman Katherine Graham told stockholders yesterday that the second quarter of 1981 is off "to a strong start" following a difficult January-March period during which profits fell sharply.

She and Washington Post Publisher Donald Graham also spoke at length about the revelation last month that a Post newspaper reporter fabricated a story about a young heroin addict and returned a Pulitzer Prize for that story when the hoax was uncovered.

The two Post executives outlined a variety of corrective actions, and Donald Graham said The Post is planning to make contributions to D.C. organizations that work to solve youth and drug problems in the wake of the scandal.

Addressing the communications company's annual meeting here, Chairman Graham said magazine division advertising business has picked up both at Newsweek and the year-old Inside Sports, with advertising revenues of the latter up 37 percent from a year ago.

Sales of advertising for the firm's four television stations also rebounded starting in March, and the broadcasting division will "have a very good second quarter," she stated.

Overall, Graham forecast that earnings for the April-June quarter should be in the "same range" as the similar period last year when The Post Co. earned $12.6 million (90 cents a share) compared with $14.5 million (92 cents, with more shares outstanding) in the 1979 quarter.

In the first quarter of 1981, Post Co., earnings fell to $1.8 million (13 cents) from $3.9 million (27 cents), mainly because of costs associated with such new ventures as Inside Sports and a television production unit. Graham said yesterday that with this sort of investment spending continuing and an unclear economic outlook, results for the full year are "even tougher to broadcast" than in 1980.

She did note that a forthcoming switch by The Washington Post newspaper to narrower newsprint will save $2.5 million a year and that a decision to delay some postage rate increases would save $4.5 million on an annual basis for Newsweek.

Graham also announced that the company's former president, Mark Meagher, would not be a candidate for re-election at the annual meeting. Although his name was included in the proxy statement, she said company lawyers had concluded that he should not stay on the board because his new job as president of Penthouse magazine involved a possible violation of antitrust laws that concern directorships of companies in the same business. o

The Post Co. chairman announced this decision with "great personal regret . . . Meagher would have added greatly to the board." She also said that no successor to Meagher has been found but that a search is in progress.

Later, stockholders of the company re-elected all other incumbent directors and one newcomer -- World Bank President Robert McNamara, the former Ford Motor Co. president and secretary of Defense, who will join the board on July 1, the day after retiring from the World Bank.

Most of the meeting was dominated by objection to editorial or advertising policies of The Post newspaper by three persons who have attended and dominated the company's annual meetings in recent years -- professional stockholder Evelyn Y. Davis; Accuracy in Media Chairman Reed Irvine, whose group monitors press performance from a conservative point of view; and Lester Kinsolving, a minister and editor of his own publication.

When Kinsolving asked if the company plans any money contributions to the District and its police department to help pay for the costs in searching for an eight-year-old boy who did not exist in the story that turned out to be a hoax, Donald Graham said the newspaper is looking "at making some kind of contribution" to youth programs.

Graham said The Post has been in contact with city officials and that an announcement of contributions would be made in a few weeks. He emphasised that the Pulitzer Prize scandal should not result in reduced attention to youth and drug problems in a city whose government faces severe spending restraints.

After Davis complained about what she described as a "lack of supervision" in the newsroom, Graham also said that the company's personnel policies have been changed to require a check on job applicants' credentials in the future. The former reporter involved in the recent hoax, Janet Cooke, had lied abut her educational background.

Graham also said that in the future, editors will ask reporters for names of confidential sources and that the exceptions to this policy would be few and that they would have to be approved by Executive Editor Benjamin C. Bradlee.

Graham said there has been "too much" of unattributed quotations and information in The Post and that a major effort has been started to print names of sources in all possible cases as part of a "period of self-examination."