Abstract
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.