изоморфизм

Construction of All Minimal Edge Extensions of the Graph with Isomorphism Rejection

Authors: Abrosimov M. B., Lobov A. A., Sudani H. H.

In 1993 Frank Harary and John P. Hayes proposed a graph model for investigating edge fault tolerance of discrete systems. The technical system is mapped to a graph. The elements of the system correspond to the vertices of the graph, and links between the elements correspond to edges or arcs of the graph. Failure of a system element refers to the removal of the corresponding vertex from the system graph along with all its edges. The formalization of a fault tolerant system implementation is the extension of the graph.

On Definability of Universal Graphic Automata by Their Input Symbol Semigroups

Authors: Farakhutdinov R. A., Molchanov V. A.

Universal graphic automaton Atm(G, G′ ) is the universally attracting object in the category of automata, for which the set of states is equipped with the structure of a graph G and the set of output symbols is equipped with the structure of a graph G′ preserved by transition and output functions of the automata. The input symbol semigroup of the automaton is S(G, G′ ) = End G×Hom(G, G′ ). It can be considered as a derivative algebraic system of the mathematical object Atm(G, G′ ) which contains useful information about the initial automaton.

Construction of All Nonisomorphic Minimal Vertex Extensions of the Graph by the Method of Canonical Representatives

Authors: Abrosimov M. B., Kamil I. A., Lobov A. A.

In 1976 John P. Hayes proposed a graph model for investigating the fault tolerance of discrete systems. The technical system is mapped to a graph. The elements of the system correspond to the vertices of the graph, and links between the elements correspond to edges or arcs of the graph. Failure of a system element refers to the removal of the corresponding vertex from the system graph along with all its edges. Later together with Frank Harary the model was extended to links failures. The formalization of a fault-tolerant system implementation is the extension of the graph.