* Tropical Storm Hermine moves towards Mexico-Texas border
* Dollar index rises, European stocks slip
* Coming Up: U.S. employment index for August; 1400 GMT
(Updates prices, adds quotes)
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 0.6 percent against a basket of currencies <.DXY>, and Hermine's forecast path kept it away from major oil and gas installations in the Gulf of Mexico. A stronger dollar can weigh on oil as it makes crude more expensive for other currency holders.
"There's a quiet week ahead in terms of fundamental news, so keep an ear to equities and the dollar," said Stephen Schork of energy consultants Schork Group, in a report.
U.S. crude <CLc1> fell $1.25 a barrel to $73.35 as at 0933 GMT. Brent crude <LCOc1> was down 77 cents from Monday's close to $76.10.
The New York Mercantile Exchange (NYMEX), home to U.S. crude futures also known as WTI, will issue one settlement for trades from Sunday, Monday and Tuesday because of Monday's Labor Day holiday.
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. Labor Day 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 deeper, 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 in the range of $75-$77.
Brent remained at an atypical premium to U.S. crude as brimming U.S. inventories weighed on the U.S. benchmark and because of strong values for Brent-related crudes, such as Russia's Urals. <CL-LCO1=R>.
European shares slipped on Tuesday, with banks down on renewed jitters about the health of the sector.
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. (With reporting by Alejandro Barbajosa; Editing by Alison Birrane and Jane Baird)