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Particle dynamics in branched systems, such as networks and lattices are of importance in many topics of physics such as optics, acoustics, condensed matter and polymer physics. Particle and wave transport in such systems can be effectively modeled using the evolution equation on so-called metric graphs. Earlier, the Schrödinger equation on a metric graph was subject of extensive research (see review papers [1-8] and references therein). The nonlinear wave equation on metric graphs has also attracted much attention recently [9-16]. Graphs are the systems consisting of bonds which are connected at the vertices. The bonds are connected according to a rule, which is called the topology of a graph. The topology of a graph is given in terms of the adjacency matrix [1, 2]:

Kicked particle dynamics in quantum graphs