cop-edge critical generalized petersen and paley graphs

Cop robber game is a two player game played on an undirected graph. in this game, the cops try to capture a robber moving on the vertices of the graph. the cop number of a graph is the least number of cops needed to guarantee that the robber will be caught. we study textit{cop-edge critical} graphs, i.e. graphs $g$ such that for any edge $e$ in $e(g)$ either $c(g-e)< c(g)$ or $c(g-e)>c(g)$. in this article, we study the edge criticality of generalized petersen graphs and paley graphs.