  A numeric function $\rho$: $\rho(k)=1+\frac{k-1}{k+1}, k \in N$ was
considered in [1]. In its terms criterions of finite representability and
tameness of marked quivers, posets with equivalence and dyadic posets can be
obtained; Dynkin schemes and extended schemes also can be characterized.
  In this paper authors consider the connection of function $\rho$ with
locally-scalar representations [2] of extended Dynkin graphs. Then a family of
functions $\rho_n$ is defined -- a generalization of function $\rho$, which
plays an analogous part for more wide class of graphs. Also some properties of
functions $\rho$ and $\rho_k$ are proved.
  References
  [1] L.A. Nazarova, A.V. Roiter. {\it Norm of a relation, separating functions
and representations of marked quivers.} Ukr. Math. Jour., 54(2002), No.6,
p.808-840.
  [2] S.A. Kruglyak, A.V. Roiter. {\it Locally-scalar representations of graphs
in the category of Hilbert spaces.} Prepr. Ukr. Math. Jour. (2003).
