Let G be a simple connected graph of order n and size m, vertex degree sequence d1 ≥ d2 ≥ · · · ≥ dn > 0, and let µ1 ≥ µ2 ≥ · · · ≥ µn−1 > µn = 0 be the eigenvalues of its Laplacian matrix. Laplacian energy LE, Laplacian-energy-like invariant LEL and Kirchhoff index K f , are graph invariants defined in terms of Laplacian eigenvalues. These are, respectively, defined as LE(G) = ∑n i=1 ∣∣∣µi − 2mn ∣∣∣, LEL(G) = ∑n−1i=1 √µi and K f (G) = n ∑n−1 i=1 1 µi . A vertex–degree–based topological index referred to as degree deviation is defined as S(G) = ∑n i=1 ∣∣∣di − 2mn ∣∣∣. Relations between K f and LE, K f and LEL, as well as K f and S are obtained