Abstract
In the game of Cops and Robbers on a graph \(G=(V,E)\), k cops try to catch a robber. The minimum number of cops required to win is called the cop number, denoted by c(G). For a planar graph G, it is known that \(c(G)\le 3\). It is a conjecture that the regular dodecahedral graph of order 20 is the smallest planar graph whose cop number is three. As the very first attack on this conjecture, we provide the following evidences in this paper: (1) any planar graph of order at most 19 has the winning vertex at which two cops can capture the robber, and (2) a special planar graph of order 19 that is constructed from the regular dodecahedral graph has the cop number of two.
Sign-in/Register to access full text options 
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 callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
