  Quantifying uncertainty is a key stage in active simultaneous localization
and mapping (SLAM), as it allows to identify the most informative actions to
execute. However, dealing with full covariance or even Fisher information
matrices (FIMs) is computationally heavy and easily becomes intractable for
online systems. In this work, we study the paradigm of active graph-SLAM
formulated over \textit{SE(n)}, and propose a general relationship between the
FIM of the system and the Laplacian matrix of the underlying pose-graph. This
link makes possible to use graph connectivity indices as utility functions with
optimality guarantees, since they approximate the well-known optimality
criteria that stem from optimal design theory. Experimental validation
demonstrates that the proposed method leads to equivalent decisions for active
SLAM in a fraction of the time.
