Unicyclic Graphs with Minimal Energy

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On a Conjecture about Tricyclic Graphs with Maximal Energy (2013, background): “In the meantime, a large number of results were obtained on the minimal energies for distinct classes of graphs, such as acyclic conjugated graphs [25, 32], bipartite graphs [30], unicyclic graphs [13,23], bicyclic graphs [14], tricyclic graphs [26,27] and tetracyclic graphs [24].”
Energy of digraphs (2008, background): “Unicyclic digraphs with extremal energy In [7] and [9] the authors considered the problem of finding the maximal and minimal energy among unicyclic graphs with a fixed number of vertices.”
Unicyclic graphs with maximal energy (2002, background): “Recently the unicyclic graphs with minimal energy were characterized [9].”
Complete solution to a problem on the maximal energy of unicyclic bipartite graphs (2010, unknown): “Similarly, one can generalize the quasi order to the cases of bipartite graphs (e.g. [15]) and unicyclic graphs (e.g. [9]).”
Maxima and Minima of the Hosoya Index and the Merrifield-Simmons Index (2010, background): “While permanents are not particularly convenient for computational purposes, they often serve as auxiliary tools, for instance to obtain recursive relations for the Hosoya index, see [49, 51, 52, 78, 79, 80, 81, 103, 106, 107].”