Abstract
We introduce the game of Surrounding Cops and Robbers on a graph, as a variant of the original game of Cops and Robbers. In contrast to the original game in which the cops win by occupying the same vertex as the robber, they now win by occupying each of the robber’s neighbouring vertices. We denote by σ(G) the surrounding cop number of G, namely the least number of cops required to surround a robber in the graph G. We present a number of results regarding this parameter, including general bounds as well as exact values for several classes of graphs. Particular classes of interest include product graphs, graphs arising from combinatorial designs, and generalised Petersen graphs.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
