* Dollar index rises, European stocks slip
* Tropical Storm Hermine has not disrupted Gulf oil output
* Coming Up: U.S. employment index for August; 1400 GMT
(Updates prices, adds quotes from paragraph 3)
By Dmitry Zhdannikov and Alex Lawler
LONDON, Sept 7 (Reuters) - Oil fell by over $1 to near $73 a barrel on Tuesday as the dollar strengthened and Tropical Storm Hermine showed no signs of disruption to crude or refining output as it came ashore near the Mexico-Texas border.
The dollar was up 0.7 percent against a basket of currencies <.DXY>. A strong dollar can weigh on oil as it makes crude more expensive for other currency holders. European stocks fell and Wall Street was expected to open lower.
"Equities came off, the dollar is strong -- it's pretty much a knock-on effect," said Rob Montefusco, a trader at Sucden Financial.
U.S. crude <CLc1> fell $1.55 a barrel to $73.05 as at 1240 GMT. Brent crude <LCOc1> was down 82 cents from Monday's close to $76.05. There was no settlement price for U.S. crude on Monday because of the Labor Day holiday.
Brent remained at an atypical premium to U.S. crude as brimming U.S. inventories weighed on the U.S. benchmark <CL-LCO1=R>. Physical crude markets in Europe are relatively strong in part because of a tight export programme for Russian crude Urals.
European shares slipped on Tuesday, with banks down on renewed jitters about the health of the sector. Futures pointed to a lower opening on Wall Street <.N>.
The Atlantic hurricane season runs from June 1 through Nov. 30 and is at its peak period. Traders watch out for storms because the Gulf is home to about 30 percent of U.S. oil output and more than 43 percent of refinery capacity.
Tropical Storm Hermine formed early on Monday and made landfall in northern Mexico near the U.S. border, according to the U.S. National Hurricane Center.
In the Atlantic, the remnants of Tropical Storm Gaston moved westward and had a medium chance of reforming as a tropical cyclone during the next 48 hours, according to the NHC.
Paul Harris, head of natural resource risk management at Bank of Ireland, said volumes were likely to remain light the day after the U.S. holiday and because of a tube strike in London.
Volumes may pick up closer to the release of U.S. employment trends data at 1400 GMT. Should data show more negative trends, the market was still unlikely to fall much further, said Harris.
"Just because we are at the peak of the hurricane season ... the market will be very reluctant to aggressively sell down," said Harris, who sees Brent crude trading in a range of $75-$77.
Monday marked the end of the U.S. driving season, the period when gasoline demand rises as people go on vacation. This, and high unemployment in the world's top consumer, raised concern about the outlook for demand.
"Figures (from the United States) started to be a little better... But there is still no job creation, there is still a lot a debt around," Montefusco said. "The only pick up we are getting is coming out of Asia." (With additional reporting by Alejandro Barbajosa; Editing by Alison Birrane and Jane Baird)