The gasoline lines have dwindled, the panic has eased and, in Fairfax County yesterday, the politicians quibbled over who should get the credit in this election year.

The trouble started yesterday morning at an executive session of the Fairfax County Board of Supervisors, a meeting closed to the press.

Board Chairman John F. Herrity, a Republican, announced to his six colleagues that he had invited Gov. John N. Dalton, also a Republican, to Fairfax for a public discussion of gasoline supplies in August and home heating oil supplies for the winter.

Democratic supervisors immediately became "furious," according to Martha V. Pennino (D-, Centreville).

"What he tried to do was politics. Absolutely. If the governor comes, the governor looks good because the lines are shorter. Herrity looks good, too," Pennino said.

Alan H. Magazine (D-Mason) told Herrity at the meeting that he was turning energy into a "political football."

"No matter what issue we are together on, Herrity goes off on his own to showboat," Magazine said.

Even Republican Supervisor Marie B. Travesky (Springfield) didn't like the idea of the governor coming to Fairfax. She suggested that the county instead invite state energy chief George Jones to discuss why the state was slow to give Northern Virginia its share of state setaside gasoline in recent weeks.

Travesky refused to say whether she became angry. "Oh, I don't want to comment on that," she said.

Facing the unanimous opposition of his fellow board members, Herrity decided at the closed meeting to "uninvite" the governor until county officials talk to Jones.

According to county figures, Northern Virginia received 31 percent less gasoline in June than in June 1978, and some 13 percent less gasoline than the rest of the state.

Later, Herrity - who once brought portable toilets into the county board room and gained wide publicity in doing so - said he would not characterize other supervisors at the morning meeting as "furious."

"Nah, I wouldn't say that. It certainly was a rather quiet meeting. If they said they were furious, then I guess they were," Herrity said.

Paul Edwards, Gov. Dalton's spokesman, said yesterday that he had talked to Herrity last week about when "it might be appropriate for the governor" to visit Northern Virginia. Edwards said the trip would be "useful to fortify the state presence in Northern Virginia."

Dalton last week came under heavy criticism from Democrats and Republicans alike for his handling of gasoline allocation withn the state. The governor, admitting that the area had been shortchanged, recently ordered that 4 million gallons of state setsside gasoline be sent to Northern Virginia this month.

Both Edwards, speaking for the governor, and Herrity, speaking for himself, said yesterday they are not interested in staging a "media event" to claim credit for shortening gasoline lines.

Disputing charges by other supervisors that he scheduled the meeting in order to "showboat," Herrity said yesterday, "I don't think there is any benefit to having a dog-and-pony show,"

In other action yesterday, the supervisors unanimously approved an emergency measure raising taxicab fares. It raised the fare for the first two-sevenths of a mile from 60 cents to 90 cents. The existing fare of 10 cents for each subsequent one-seventh of a mile was unchanged.

In a hearing on a proposed ban against installing gasoline and diesel fuel tanks in private homes, the supervisors were told yesterday that many "bootleg tanks" are being installed in the county by "dreadfully unqualified" people.

Harry B. Lyon, a petroleum operation engineer, said the tanks are dangerous and, in the case of diesel fuel tanks, are used to defraud the state and federal government of tax money. He said many county residents buy Number Two heating oil, which is essentially the same as diesel fuel, store it in tanks at their homes and use it in their diesel-powered cars without paying taxes required for such use.

The board last month passed an emergency ordinance banning the tanks, and yesterday postponed passage of a permanent ordinance.