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 | ( ) ( ) | 1 deg u deg v   . A subset D of ( ) V G is called an equitable independent set if for any , u D v   ( ) e N u for all { } v D u   . The concept of equi independent equitable domination is a combination of these two important concepts. ...

an equitable domination has interesting application in the contextof social networks. in a network, nodes with nearly equal capacitymay interact with each other in a better way. in the societypersons with nearly equal status, tend to be friendly. in thispaper, we introduce new variant of equitable domination of agraph. basic properties and some interesting results have beenobtained.

A subset D of V (G) is called an equitable dominating set of a graph G if for every v ∈ (V − D), there exists a vertex u ∈ D such that uv ∈ E(G) and |deg(u) − deg(v)| 6 1. The minimum cardinality of such a dominating set is denoted by γe(G) and is called equitable domination number of G. In this paper we introduce the equitable edge domination and equitable edge domatic number in a graph, exact...

Let G = (V,E) be a connected graph, An equitable dominating S of a graph G is called the neighborhood connected equitable dominating set (nced-set) if the induced subgraph 〈Ne(S)〉 is connected The minimum cardinality of a nced-set of G is called the neighborhood connected equitable domination number of G and is denoted by γnce(G). In this paper we initiate a study of this parameter. For any gra...

a dominating set $d subseteq v$ of a graph $g = (v,e)$ is said to be a connected cototal dominating set if $langle d rangle$ is connected and $langle v-d rangle neq phi$, contains no isolated vertices. a connected cototal dominating set is said to be minimal if no proper subset of $d$ is connected cototal dominating set. the connected cototal domination number $gamma_{ccl}(g)$ of $g$ is the min...