  In this work, we fully define the existing relationships between traditional
optimality criteria and the connectivity of the underlying pose-graph in Active
SLAM, characterizing, therefore, the connection between Graph Theory and the
Theory Optimal Experimental Design. We validate the proposed relationships in
2D and 3D graph SLAM datasets, showing a remarkable relaxation of the
computational load when using the graph structure. Furthermore, we present a
novel Active SLAM framework which outperforms traditional methods by
successfully leveraging the graphical facet of the problem so as to
autonomously explore an unknown environment.
