Abstract
A unicyclic graph is a connected graph whose number of edges is equal to the number of vertices. Hou (J Math Chem 29:163–168, 2001) first considered the minimal energy for general unicyclic graphs. In this paper, we determine the unicyclic graphs with the minimal energy in \({\mathcal {U}_n^l}\) and the unicyclic graphs with the first forth smallest energy in \({\mathcal {U}_n\,(n\geq 13)}\) vertices.
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Liu, Y. Some results on energy of unicyclic graphs with n vertices. J Math Chem 47, 1–10 (2010). https://doi.org/10.1007/s10910-009-9528-2
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DOI: https://doi.org/10.1007/s10910-009-9528-2