Let G be a finite group of order n. The strong power graph Ps(G) of G is the undirected graph whose vertices are the elements of G such that two distinct vertices a and b are adjacent if am1=bm2 for some positive integers m1, m2 < n. In this article we classify all groups G for which Ps(G) is a line graph. Spectrum and permanent of the Laplacian matrix of the strong power graph Ps(G) are found for any finite group G.
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