  Let $G=(V,E)$ be a simple graph. A dominating set of $G$ is a subset
$D\subseteq V$ such that every vertex not in $D$ is adjacent to at least one
vertex in $D$. The cardinality of a smallest dominating set of $G$, denoted by
$\gamma(G)$, is the domination number of $G$. A dominating set $D$ is called
co-even dominating set if the degree of vertex $v$ is even number for all $v\in
V-D$.
  The cardinality of a smallest co-even dominating set of $G$, denoted by
$\gamma _{coe}(G)$, is the co-even domination number of $G$. In this paper we
study co-even domination number of graphs which constructed by some operations
on a vertex or an edge of a graph.
