# Cop-edge critical generalized Petersen and Paley graphs

Document Type : Original paper

Authors

1 HRIST (Deemed to be university), Bengaluru-560029, Karnataka

2 Adam Mickiewicz University, Poznan, Poland

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

Main Subjects

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