Vulnerability is the most important concept in analysis of communication networks to disruption. Any network can be modelled by graphs. So measures defined on graphs gives an idea in design. Integrity is one of the well-known vulnerability measures interested in remaining structure of a graph after any failure. Domination is also an another popular concept in network design. Nowadays new vulnerability measures take a great role in network design. Recently designers take into account of any failure not only on nodes also on links which have special properties. A new measure edge domination integrity of a connected and undirected graph was defined by E. Kılıç and A. Beşirik such as ${DI}^{'}(G)=min{ |S|+m(G-S):S subseteq E(G)}$ where $m(G-S)$ is the order of a maximum component of $G-S$ and $S$ is an edge dominating set. In this paper some results concerning this parameter on corona products of graph structures $P_n odot P_m $, $ P_n odot C_m$, $P_n odot K_{1,m}$ are presented.