Prince William County Executive Clinton B. Mullen yesterday proposed a $26.7 million county government operating budget for 1977-78, which would require an increase of 55 cents per $100 of assessed valuation in the county's real estate tax rate.

Mullen stressed that he is not recommending the tax increase, which would mean that the tax bill on a $45,000 home in Prince William County would jump from $652.50 to $735. The current real estate tax rate is $4.35 for each $100 of assessed valuation.

Mullen said there are "too many ifs" at this point to determine what the final tax increase may be. He noted that county school board has not yet completed its budget.

A spokesman for the county government said that because of various undetermined factors, such as the total of the school budget and additional construction funds that may be needed, the tax rate "could go up even more than (55 cents)." Each 10-cent increase in the tax rate yields $667,000 for the county treasury, the spokesman said.

County Board Chairwoman Alice E. Humphries said yesterday it appears the Board may have to set a tentative tax rate increase before it receives the proposed school budget. During the current year, schools accounted for 55 per cent of the total county budget.

Mullen's proposed budget would create 114 new jobs in the county government, including 19 in the sheriff's department, 34 in mental health agencies, and six for new police officers.

The county executive also recommended tht the county library cut its hours of operation from 64 to 48 hours a week to save money.

Most of the 11 per cent budget increase would go for personnel and wage increases and inflation, not for the improvement of existing services, Mullen said. He said there are no new programs in the budget.

Prince William is one of the fastest-growing counties in the nation. Its population of 50,000 in 1960 had tripled by 1974. The county planning office predicts that the county may have 161,000 residents by 1980.

The county attracted many federal government workers who were unable to afford more costly housing in the District and the inner suburbs. The average house in Prince William County last year cost in the mid-$40,000 range, according to the county spokesman.

Between 1975 and 1976, the real estate tax rate in Prince William increased 20 per cent, from $3.62 to $4.35 per $100 of assessed valuation.

But assessment supervisor Arthur Shoemake said the "true effective tax rate," based on the total fair market values of property rather than the smaller assessed values, increased about 8.5 per cent between 1975 and 1976, from about $1.17 to $1.27 per $100 of market value. Prince William bases its tax bills on an assessment that is 33 per cent of fair market value.

In his budget message, Mullen said the Board of Supervisors needs to reassess the ability of the county's sewer and water districts to provide additional services.He said the extra sewer and water lives are "crucial to the county's orderly development and its ability to attract industrial and commercial facilities."

Mullen presented his proposed budget to the Supervisors yesterday. The Board will hold work sessions to consider Mullen's proposal before making a fianl decision on the budget, the spokesman said.

Mullen said that his proposal this year approaches the concept of a zero-based budget in which the need for each county program is reconsidered each year. The new format, he said, will be a "heck of a lot more understandable to the public."

The new budget identifies programs within each department and includes the cost to continue activities at their present level, increased costs over which Mullen has little or no control and the cost of providing increases in each service, with estimates of possible revenue sources.