A SHORT NOTE ON COPS AND ROBBERS PLAYING ON TOTAL GRAPHS

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Published: 2017-03-07

Page: 39-45


CHARLES DOMINIC

Department of Mathematics, Universidade de Aveiro, 3810-193, Aveiro, Portugal.

DOMINGOS M. CARDOSO

Department of Mathematics, Universidade de Aveiro, 3810-193, Aveiro, Portugal.

LUKASZ WITKOWSKI

Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznan, Poland.

MARCIN WITKOWSKI *

Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznan, Poland.

*Author to whom correspondence should be addressed.


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 captured. The total graph T(G) of a graph G has a vertex for each edge and vertex of G and an edge in T(G) for every edge-edge, vertex-edge, and vertex-vertex adjacency in G. In this paper, we play the game on the total graph T(G), showing in particular that c(T(G)) ≤ 3 for every planar graph G.

Keywords: Cops and robbers, vertex-pursuit games


How to Cite

DOMINIC, C., CARDOSO, D. M., WITKOWSKI, L., & WITKOWSKI, M. (2017). A SHORT NOTE ON COPS AND ROBBERS PLAYING ON TOTAL GRAPHS. Asian Journal of Mathematics and Computer Research, 16(1), 39–45. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/816

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