In this paper, the concept of minimal intuitionistic dominating vertex subset of intuitionistic fuzzy graph was considered, and on its basis the notion of a domination set as an invariant of the intuitionistic fuzzy graph was considered. A method and an algorithm for finding all minimal intuitionistic dominating vertex subset and domination set were proposed. This method is the generalization of Maghout’s method for fuzzy graphs. The example of finding the domination set of the intuitionistic fuzzy graph was considered as well. The considered method and algorithm can be used to find other invariants, in particular, externally stable set, intuitionistic base and antibase of the intuitionistic fuzzy graphs.
Keywords: intuitionistic fuzzy set, degree of belonging, degree of non-belonging, fuzzy relation, intuitionistic fuzzy graph, intuitionistic fuzzy graph of the first kind, domination set, algorithm, disjunctive member, adjacency matrix
In this paper, the concept of chromatic set of fuzzy temporal graph is introduced. Chromatic set of fuzzy temporal graph is a generalization of one side of a fuzzy, but on the other hand - temporal graphs. The degree of connectivity vertices changes in discrete time in a fuzzy temporal graph. Most of isomorphic transformations of fuzzy temporal graph change their external representation without changing its signature. In this regard, matters relating to the consideration of temporal invariants of fuzzy graphs. Example of finding chromatic sets of fuzzy temporal graph is considered here.
Keywords: Fuzzy temporal graph, fuzzy partial graph, graph coloring, chromatic set, the degree of separability