Abstract
Fuzzy graph models enjoy the ubiquity of being in natural and human-made structures, namely dynamic process in physical, biological and social systems. As a result of inconsistent and indeterminate information inherent in real-life problems which are often uncertain, it is highly difficult for an expert to model those problems based on a fuzzy graph. Intuitionistic fuzzy graph (IFG) can deal with the uncertainty associated with the inconsistent and indeterminate information of any real-world problem, where fuzzy graphs may fail to reveal satisfactory results. Likewise, IFG has an important role in neural networks, computer network, and clustering. In the design of a network, it is important to analyze connections by the levels. In this paper, we describe d-regular, td-regular, m-highly irregular and m-highly totally irregular IFGs and prove the necessary and sufficient conditions which under this conditions the d-regular and td-regular IFGs are equivalent. Also, a comparative study between m-highly irregular IFG and m-highly totally irregular IFG are given.
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