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For a non-zero real number α, let sα(G) denote the sum of the αth power of the non-zero Laplacian eigenvalues of a graph G. In this paper, we establish a connection between sα(G) and the first Zagreb index in which the Hölder’s inequality plays a key role. By using this result, we present a lot of bounds of sα(G) for a connected (molecular) graph G in terms of its number of vertices (atoms)...
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