Abstract. Quantum graph of Sierpinski gasket type with attached leadsin an electric eld is considered. We study the dependence of the trans-mission coecient via the wave number of the quantum particle. It hasstrongly resonance character. The inuence of the amplitude and theorientation of the electric eld on the coecient is investigated. 1. IntroductionBefore the beginning of the twentieth century continuous mathematical ob-jects were the main tool for scienti c investigations. Classical analysis estab-lished a numerous new directions such as topology, di erential geometry, func-tional and harmonic analysis and many others. That directions are activelydeveloped in our days and seemingly will be dominating directions in the eldof mathematical sciences in future.At the same time, it has become clear that objects of nature has muchmore irregular structure than the objects of the classical analysis. A specialinterest is attracted by self-similar sets, or, as they are called, fractals (self-similarity, generally speaking, does not necessarily mean a linear similarity, andits synonym in this case is the word \like). Of course, self-similar sets werestudied in analysis earlier (e.g., the well-known Cantor set). But the intensiveinvestigation started after the publication in 1977 of Mandelbrot book \TheFractal Geometry of Nature [12] where the term \fractal was introduced.One can observe self-similarity in nature for di erent objects, e.g., leaves,trees, or patterns on animal skins. However, no existing object is completelyself-similar, so fractals are only an approximation of real objects. Note thateven a small change in the set of fractal parameters changes it dramatically, forexample, leaf of fern and Sierpinski gasket presented in Figure 1, are fractalsof the same type, di ering by only a few parameters.To describe physical phenomena related with the fractal-like objects, oneneeds the \analysis on fractals. For example, the thermal di usion is described