  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 $G$ with
respect 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 of
generalised Cayley graphs and the twisted Cayley sum graphs under some
conditions. These extend a result of Frankl to such graphs. Using the above
bounds and a result of Bollob\'{a}s--Janson--Riordan, we show that the weak
Meyniel's conjecture holds for these algebraic graphs.
