Nevada, bolstered by a resurgent tourist industry, enjoyed the fastest income growth of any state through the third quarter of last year while Wyoming and several other energy states had the weakest income growth, the government reports.

The Commerce Department said that non-farm incomes rose 7.8 percent nationally in the 12 months ending with September 1988, virtually identical to the 7.7 percent rise in incomes overall posted for the period ending with the second quarter.The national average masked wide disparities among states and regions of the country.

Nevada, which is enjoying a construction boom fueled by good times in the tourism industry, saw incomes shoot up 12.9 percent, the biggest percentage increase for any state.

This was followed by a 9.9 percent gain in non-farm incomes in New Hampshire and a 9.6 percent rise in Hawaii. Also posting large increases were Massachusetts and Florida, both at 9.3 percent.

With inflation rising at an annual rate of 4.4 percent last year, the figures showed that these states stayed well ahead of the increase in prices.

At the other end of the scale, income growth in some states just barely kept up with the rise in prices.

Wyoming ranked last with a 4.2 percent rise in non-farm incomes over the period ending with the third quarter, followed by Alaska with a 4.8 percent increase. Other states with low income growth were Colorado, 5.2 percent; North Dakota, 5.3 percent; New Mexico, 5.3 percent, and West Virginia, 5.8 percent.

Commerce Department analyst Rudolph DePass said that the slow income-growth states had all been held back by depressed conditions in the energy sector.

"We are still seeing the effects of weak energy prices," he said. "While some states have been able to diversify their economies, others have not."

By region, New England continued to lead the rest of the nation, with an overall income growth of 8.9 percent.

DePass said this increase was occurring even though defense spending, which had spurred growth in the region's high-technology industries, slowed in the last year.

The Far West was second with an income growth of 8.7 percent.

Critics of economic policies during the Reagan years have charged that the recovery was essentially a bi-coastal expansion, with both coasts doing well while America's heartland suffered.

Other regions of the country and their income growth rates were:

Southeast, 8.1 percent; Mid-Atlantic, 7.9 percent; Plains, 7.4 percent; Great Lakes, 7.2 percent; Southwest, 6.9 percent, and Rocky Mountains, 6.1 percent.

The Commerce Department focuses on changes in non-farm income as a better indication of a region's prosperity because of the often erratic nature of farm incomes.