%0 Journal Article %T Cop-edge critical generalized Petersen and Paley graphs %J Communications in Combinatorics and Optimization %I Azarbaijan Shahid Madani University %Z 2538-2128 %A Dominic, Charles %A Witkowski, Łukasz %A Witkowski, Marcin %D 2023 %\ 06/01/2023 %V 8 %N 2 %P 359-378 %! Cop-edge critical generalized Petersen and Paley graphs %K Cops and Robbers %K vertex-pursuit games %K Petersen graphs %K Paley graphs %R 10.22049/cco.2022.27308.1229 %X 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.  %U http://comb-opt.azaruniv.ac.ir/article_14372_cda32bc81b5eb18af77d2afc3c8e25cd.pdf