## Operations on fuzzy graphs.(English)Zbl 0804.05069

Different operations with graphs $$G_ 1$$ and $$G_ 2$$ yield $$G = g(G_ 1, G_ 2)$$. Under a certain hypothesis, necessary and sufficient conditions are derived for ensuring that the application of $$g$$, on two fuzzy subgraphs (fsg) of $$G_ 1$$ and $$G_ 2$$, provides a fsg of $$G$$. A proposition establishes when a fsg of $$G$$ may be represented by the application of $$g$$ on fsg’s of $$G_ i$$, $$i=1,2$$. This result is obtained when $$g$$ is the Cartesian product, the composition, the union or the join of $$G_ 1$$ and $$G_ 2$$. The authors define strong fsg’s and give conditions that ensure that such fsg’s of $$G_ i$$, $$i=1,2$$, have the same property under the use of $$g$$. Different examples are discussed.

### MSC:

 05C99 Graph theory 94C15 Applications of graph theory to circuits and networks

### Keywords:

fuzzy graph; completeness; bigraphs; operations; fuzzy subgraphs
Full Text:

### References:

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