We associate a particular type of interval-valued fuzzy graph(IVFG) called interval-valued fuzzy identity graph(IVFIG) with every finite group and study its various properties. We show that IVFIG associated with a finite group is not unique. We also show that every IVFIG associated with a finite group is a strong IVFG. It does not contain any feeble or weak arcs. Further, it is strongly connected. We prove that the IVFIG associated with a finite group in which every element is self inversed is an interval-valued fuzzy tree and the IVFIG of Zn (n is odd) under addition modulo n is the disjoint union of interval-valued fuzzy cycles.
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