New Asymptotic and Algorithmic Results in Calculation of Random Graphs Connectivity

This paper is devoted to calculations of connectivity probabilities and distributions of connectivity components numbers in planar and recursively defined and parallel-sequential random graphs. These calculations are based on asymptotic formulas for connectivity probabilities and on recurrent relations for different deterministic and stochastic characteristics of random graphs and on limit theorems for Markov chains with finite state set. Main aim of these paper is to decrease calculational complexity of considered problems solutions. Key–Words: Planar graph, cross section, connectivity probability, recursive definition, calculational complexity, central limit theorem, law of large numbers.