Abstract
Fuzzy graph theory is finding an increasing number of application in modeling real time systems where the level of information inherent in the system varies with different levels of precision. Special fuzzy graph can be obtained from two given fuzzy graphs using the operations beta products. In this paper, we introduce the notions of some kinds of beta product of two fuzzy graphs. The concept of strong, regular and complement of [Formula: see text]-product of two fuzzy graphs and relation between them are also obtained. At the end, an application with a cryptographic object is said to be using the [Formula: see text]-product of fuzzy graphs.
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