The energy of a graph is defined as the sum of the absolute values of all the eigenvalues of the graph. For a given positive integer d with \(3\leqslant d\leqslant n-2\), we characterize the graphs with minimal energy in the class of unicyclic graphs with n vertices and a given diameter d.
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Li, F., Zhou, B. Minimal energy of unicyclic graphs of a given diameter. J Math Chem 43, 476–484 (2008). https://doi.org/10.1007/s10910-006-9209-3
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DOI: https://doi.org/10.1007/s10910-006-9209-3