### Rodionov A.S.

## Reliability polynomials of random graphs: obtaining and use

Some problemjs of obtaining and usage of reliability polynomials of random graphs with unreliable edges are discussed. The presentation of reliability plynomials with most informative coefficients is used, such that some of coefficients can be obtained without calculations or with minimal cost by using their meaning, thus significantly speeding up the calculation process. Along with well-known polynomial for all-terminal reliability, polynomials for average pairwise reliability and average size of a connected subgraph contains some marked vertex are examined. The unified approach for obtaining all these polynomials is used that is based on the factorisation method, reduction of a graph dimension and exact finit expressions for graphs of small dimension or of some special kind. The problems of usage of relyability polynomials for a network analysis and\or structural optimization are discussed also.

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