The complements of path and cycle are determined by their distance (signless) Laplacian spectra

摘要

Let G be a connected graph with vertex set V(G) and edge set E(G). Let T(G) be the diagonal matrix of vertex transmissions of G and D(G) be the distance matrix of G. The distance Laplacian matrix of G is defined as . The distance signless Laplacian matrix of G is defined as . In this paper, we show that the complements of path and cycle are determined by their distance (signless) Laplacian spectra.