UDC 530.12:539.12 A Particular Case of a Sequential Growth of an X-Graph A. L. Krugly Department of Applied Mathematics and Computer Science Scientific Research Institute for System Analysis of the Russian Academy of Science 36, k. 1, Nahimovskiy pr., Moscow, Russia, 117218 A particular case of discrete spacetime on a microscopic level is considered. <...> The model is a directed acyclic dyadic graph (an x-graph). <...> The dyadic graph means that each vertex possesses no more than two incident incoming edges and two incident outgoing edges. <...> The sequential growth dynamics of this model is considered. <...> This dynamics is a stochastic sequential addition of new vertices one by one. <...> It is proved that the algorithm to calculate probabilities of this dynamics is a unique solution that satisfies some principles of causality, symmetry and normalization. <...> The first step is the choice of the addition of the new vertex to the future or to the past. <...> By definition, the probability of this choice is 1/2 for both outcomes. <...> The second step is the equiprobable choice of one vertex number V . <...> Then the probability is 1/N, where N is a cardinality of the set of vertices of the x-graph. <...> If we choose the direction to the future, the third step is a random choice of two directed paths from the vertex number V . <...> If we choose the direction to the past, we must randomly choose the two inversely directed paths from the vertex number V . <...> The iterative procedure to calculate probabilities is considered. <...> Key words and phrases: causal set, random graph, directed graph. 1. <...> Introduction By assumption spacetime is discrete on a microscopic level. <...> This is a directed acyclic dyadic graph. <...> The dyadic graph means that each vertex possesses no more then two incident incoming edges and two incident outgoing edges. <...> The vertex with 4 incident edges forms an x-structure. <...> These free valences are called external edges as external lines in Feynman diagrams. <...> There are two types of external edges: incoming external edges and outgoing external edges. <...> The number of incoming external edges is equal to the number of outgoing external edges for any x-graph. <...> We start from some given x-graph and add new vertices one by one. <...> This procedure is called ‘a classical sequential growth dynamics’. <...> We can <...>