The Laplacian-energy like invariant is an energy like invariant

摘要

Short time ago Liu and Liu [MATCH Commun. Math. Comput. Chem. 59 (2008) 355-372] put forward a so-called Laplacian-energy like invariant (LEL), defined as the sum of the square roots of the Laplacian eigenvalues. From its name, one could get the impression that the properties of LEL are similar to those of the Laplacian energy LE. However, already the inventors of LEL realized that LEL resembles much more the ordinary graph energy (E) than LE. We now provide further arguments supporting this conclusion. In particular, numerous earlier obtained bounds and approximations for E can be simply "translated" into bounds and approximations for LEL.