Permanental energy of any m-edge graph is at least 2√m, with equality if and only if the graph is a star plus isolated vertices.
On the permanental nullity and matching number of graphs.Linear and Multilinear Algebra, 66(3):516– 524
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Permanental Energy of Graphs
Permanental energy of any m-edge graph is at least 2√m, with equality if and only if the graph is a star plus isolated vertices.