  Research involving computing with mobile agents is a fast-growing field,
given the advancement of technology in automated systems, e.g., robots, drones,
self-driving cars, etc. Therefore, it is pressing to focus on solving classical
network problems using mobile agents. In this paper, we study one such problem
-- finding small dominating sets of a graph $G$ using mobile agents. Dominating
set is interesting in the field of mobile agents as it opens up a way for
solving various robotic problems, e.g., guarding, covering, facility location,
transport routing, etc. In this paper, we first present two algorithms for
computing a {\em minimal dominating set}: (i) an $O(m)$ time algorithm if the
robots start from a single node (i.e., gathered initially), (ii) an
$O(\ell\Delta\log(\lambda)+n\ell+m)$ time algorithm, if the robots start from
multiple nodes (i.e., positioned arbitrarily), where $m$ is the number of edges
and $\Delta$ is the maximum degree of $G$, $\ell$ is the number of clusters of
the robot initially and $\lambda$ is the maximum ID-length of the robots. Then
we present a $\ln (\Delta)$ approximation algorithm for the {\em minimum}
dominating set which takes $O(n\Delta\log (\lambda))$ rounds.
