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In this article, we study the game of cops and robbers in algebraic graphs.We show that the cop number of the Cayley sum graph of a finite group $G$ withrespect to a subset $S$ is at most its degree when the graph is connected,undirected. We also show that a similar bound holds for the cop number ofgeneralised Cayley graphs and the twisted Cayley sum graphs under someconditions. These extend a result of Frankl to such graphs. Using the abovebounds and a result of Bollob\'{a}s--Janson--Riordan, we show that the weakMeyniel's conjecture holds for these algebraic graphs.

On the cop number and the weak Meyniel's conjecture for algebraic graphs