Abstract:

The lexicographic product of two fuzzy graphs and gives some necessary or sufficient conditions are given under which a fuzzy graph can be decomposited into a strong product, direct and lexicographic product of two fuzzy graphs. It is proved that the strong product, direct product or lexicographic product of partial fuzzy subgraphs of two fuzzy graphs is a partial fuzzy subgraph of strong product, direct product or lexicographic product of the two fuzzy graphs. Some isomorphism theorems on these products of fuzzy graphs are also obtained.

Key words: fuzzy graph; decomposition; cartesian product; strong product; direct product; lexicographic product; isomorphism