The energy of a graph is defined as the sum of the absolute values of its graph eigenvalues (i.e., the sum of its graph spectrum terms). Other varieties of graph energy are defined analogously using different matrices associated with a graph (and in particular, a weighted adjacency matrix). As summarized by Alikhani and Ghanbari, the energy of a graph cannot be an odd integer, the square root of an odd integer, or the golden ratio.
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