On fuzzification of some concepts of graphs. (English) Zbl 0934.05099

Alaoui, Assia

Fuzzy Sets Syst. 101, No. 3, 363-389 (1999).

The author discusses certain fuzzy sets which generalize the concepts of internally stable set (also known as independent set), externally stable set (also known as dominating set), not externally dominated set (which means a set of vertices such that there is no arc from outside it into it) and kernel. The structure of the fuzzy analogous is studied and it is shown that they are characterized as solutions of certain mathematical programming problems. In some particular cases an exhaustive description of the investigated sets is obtained. The paper is remarkably self-contained. Erratum: On page 366, line 9, \(y\in A\) should be \(y\not\in A\).

Reviewer: S.Rudeanu (Bucureşti)

MSC:

05C69	Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)
05C99	Graph theory

Keywords:

fuzzy sets; independent set; dominating set; programming problems

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