On distance signless Laplacian spectrum of the complements of unicyclic graphs and trees

Let Gbe a connected graph, we define D-Q(G) = Tr(G) + D(G) as distance signless Laplacian matrix of G, where Tr(G) and D(G) are diagonal matrix with vertex transmissions of Gand distance matrix of G, respectively. In this paper, we characterize the extremal graphs which maximize the D-Q-spectral radius among complements of unicyclic graphs and trees, respectively. And we also characterize the unique graph among complements of unicyclic graphs of diameter three which maximize the least D-Q-eigenvalues. (c) 2021 Elsevier Inc. All rights reserved.