Finding minimal vertex extensions of a colored undirected graph

Background. The research considers the results of the finding minimal vertex extensions of the colored undirected graphs. This topic relates to the modelling of the completely fault tolerant technical systems with the different typed objects in the terms of graph theory. The system could be described as some graph where vertices reflect system's objects and edges are connection lines between these objects. Fault tolerance property is one of the technical system's main properties, especially if such system works in the critical life areas: medicine, space, communication. Materials and methods. The article uses mathematical modelling methods of the technical systems in the terms of graph theory. The main research is focused on constructing non-isomorphic fault tolerant implementations of the colored undirected graphs. The constructing algorithms uses isomorphic rejection and canonical labelling techniques. Results. The article considers the problem of the search for minimal vertex k-extensions of the colored graphs without isomorphism verification. The study proposes the algorithm of finding all non-isomorphic minimal vertex k-extensions for the defined colored graph. Conclusions. The proposed algorithm was implemented as a runnable executable program. There are some experiment calculations for the various configurations of the colored graphs.