University of KashanMathematics Interdisciplinary Research2538-36394220191201Note on the Sum of Powers of Normalized Signless Laplacian Eigenvalues of Graphs17118210158710.22052/mir.2019.208991.1180ENŞ. BurcuBozkurt AltındağKonya, Turkey0000-0001-9727-6107Journal Article20191118In this paper, for a connected graph G and a real α≠0, we define a new graph invariant σ<sub>α</sub>(G)-as the sum of the alphath powers of the normalized signless Laplacian eigenvalues of G. Note that σ<sub>1/2</sub>(G) is equal to Randic (normalized) incidence energy which have been recently studied in the literature [5, 15]. We present some bounds on σ<sub>α</sub>(G) (α ≠ 0, 1) and also consider the special case α = 1/2.https://mir.kashanu.ac.ir/article_101587_6d3f9f9d05078067f97d041c27644362.pdf