Cop-edge critical generalized Petersen and Paley graphs

Communications in Combinatorics and Optimization

article

Charles Dominic¹  Łukasz Witkowski²  Marcin Witkowski² 

[1] HRIST ,(Deemed to be university);Adam Mickiewicz University

关键词: Cops and Robbers;    vertex-pursuit games;    Petersen graphs;    Paley graphs;   

DOI  :  10.22049/cco.2022.27308.1229

学科分类：社会科学、人文和艺术（综合）

来源: Azarbaijan Shahide Madani Universit

【 摘 要 】

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 $c(G-e)c(G)$. In this article, we study the edge criticality of generalized Petersen graphs and Paley graphs.

【 授权许可】

CC BY-SA