Distance Laplacian eigenvalues of graphs, and chromatic and independence number

Abstract

Given an interval I, let m D L (G) I (or simply m D L I) be the number of distance Laplacian eigenvalues of a graph G which lie in I. For a prescribed interval I, we give the bounds for m D L I in terms of the independence number α(G), the chromatic number χ, the number of pendant vertices p, the number of components in the complement graph C G and the diameter d of G. In particular, we prove thatand discuss the cases where the bounds are best possible. In addition, we characterize graphs of diameter d ≤ 2 which satisfy mWe also propose some problems of interest.