Signless Laplacian Energy of Partial Complement of a Graph

The energy E(G) of a graph G, defined as the sum of the absolute values of its eigenvalues, belongs to the most popular graph invariants in chemical graph theory. It originates from the π−electron energy in the Huckel molecular orbital model, but has also gained purely mathematical interest. Let q¹, q²,…, qn be the signless Laplacian eigenvalues of G. The signless Laplacian energy of G has recently been defined as (Formula Presented) In this paper, we define signless Laplacian energy of partial complements of a graph. Signless Laplacian spectrum of partial complements of the few classes of graphs are established. Some bounds and properties of signless Laplacian energy are obtained.