2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64172The stringy Euler number and E-function of Batyrev for log terminal singularities can in dimension 2 also be considered for a normal surface singularity with all log discrepancies nonzero in its minimal log resolution. Here we obtain a structure theorem for resolution graphs with respect to log discrepancies, implying that these stringy invariants can be defined in a natural way, even when some log discrepancies are zero, and more precisely for all normal surface singularities which are not log canonical. We also show that the stringy E-functions of log terminal surface singularities are polynomials (with rational powers) with nonnegative coefficients, yielding well defined (rationally graded) stringy Hodge numbers.22 pages, to appear in J. Alg. GeomAlgebraic Geometry14B05; 14J17; 32S50text