A study of cluster hypergraphs and its properties.

In this study, cluster hypergraphs are introduced to generalize the concept of hypergraphs, where cluster nodes are allowed. Few related terms and properties on cluster hypergraphs are discussed. Some operations, including the Cartesian product, union, intersection, etc.

Interval-valued fuzzy [Formula: see text]-tolerance competition graphs.

This paper develops an interval-valued fuzzy [Formula: see text]-tolerance competition graphs which is the extension of basic fuzzy graphs and [Formula: see text] is any real valued function. Interval-valued fuzzy [Formula: see text]-tolerance competition graph is constructed by taking all the fuzzy sets of a fuzzy [Formula: see text]-tolerance competition graph as interval-valued fuzzy sets. Product of two IVFPTCGs and relations between them are defined.