Title of article :
Cop-edge critical generalized Petersen and Paley graphs
Author/Authors :
Dominic ، Charles Department of Mathematics - HRIST (Deemed to be university) , Witkowski ، Łukasz Faculty of Mathematics and Computer Science - Adam Mickiewicz University , Witkowski ، Marcin Faculty of Mathematics and Computer Science - Adam Mickiewicz University
Abstract :
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.
Keywords :
Cops and Robbers , vertex , pursuit games , Petersen graphs , Paley graphs
Journal title :
Communications in Combinatorics and Optimization
Journal title :
Communications in Combinatorics and Optimization
