In this paper, we focus on some specific optimization problems from graphtheory, those for which all feasible solutions have an equal sizethat depends on the instance size.Once having provided a formal definition of this class ofproblems, we try to extract some of its basic properties; most ofthese are deduced from the equivalence, under differentialapproximation, between two versions of a problem π which onlydiffer on a linear transformation of their objective functions.This is notably the case of maximization and minimization versionsof π, as well as general minimization and minimization withtriangular inequality versions of π. Then, we prove that somewell known problems do belong to this class, such as special casesof both spanning tree and vehicles routing problems. Inparticular, we study the strict rural postman problem(called SRPP) and show that both the maximization and theminimization versions can be approximately solved, in polynomialtime, within a differential ratio bounded above by 1/2.From these results, we derive new bounds for standard ratiowhen restricting edge weights to the interval [a,ta] (theSRPP[t] problem): we respectively provide a 2/(t+1)- and a(t+1)/2t-standard approximation for the minimization and themaximization versions.