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A subset D of ()V G is called an equitable dominating set if for every ()v V G D , there exists a vertex u D such that ()uv E G and | ( ) ( ) | 1deg u deg v . A subset D of ()V G is called an equitable independent set if for any u D , ()ev N u for all {}v D u where, ( ) { ( ) / (),eN u v V G v N u | ( ) ( ) | 1}deg u deg v . An equitable dominating set D is said to be an equi independent equitable dominating set if it is also an equitable independent set. The minimum cardinality of an equi independent equitable dominating set is called equi independent equitable domination number which is denoted by ei. We investigated an equi independent equitable domination number for some special graphs