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In this paper we determine distance k--domination number of graph obtained by duplication of vertices altogether by edges in cycle Cn, splitting graph of cycle Cn as well as graph obtained by duplication of edges altogether by vertices in cycle Cn. [ABSTRACT FROM AUTHOR]

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 | deg(u)-deg(v) |≤1. A subset D of V(G) is called an equitable independent set if for any u∊D, v∉Ne (u) for all v∊D-{u} where, v∉Ne (u)= v∊N(u) | deg(u)-deg(v) |≤1}. 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 ie. We investigated an equi independent equitable domination number for some special graphs. [ABSTRACT FROM AUTHOR]