Abstarct: ‎ ‎Several matrices can be associated to a graph such as the distance matrix‎, ‎distance Laplacian matrix or the‎ distance signlees Laplacian matrix‎. ‎The spectrum of these matrices gives some informations about the‎ structure of the graph‎. ‎The distance signless Laplacian spectral radius of a connected graph G is the largest eigenvalue of the distance signless Laplacian matrix of G‎, ‎defined as D^Q (G)=Tr(G)+D(G), ‎where D(G)is the distance matrix of G and Tr(G) is the diagonal matrix of vertex transmissions of G. ‎In this thesis‎, ‎we determine some upper and lower bounds on the distance signless Laplacian spectral radius of G. baxsed on some graph invariants such as order‎, ‎size‎, ‎independence number and matching number‎. ‎The graphs attaining the corresponding bounds are also characterized‎. ‎Further‎, ‎we study the distance signless‎ ‎Laplacian spectrum of some graphs obtained by operations‎. ‎In addition‎, ‎we define distance signless Laplacian energy and give some upper and lower bounds on the distance signless Laplacian energy of graphs‎. ‎We also propose a Brouwer-type conjecture for the sum of k- largest distance signless Laplacian eigenvalues and show that it holds for graphs of diameter one and graphs of diameter two for all k. ‎We then show that it holds for k=n-1 and k=n for all graphs and for some k for r-transmission regular graphs‎. ‎We conclude by giving some alternative directions and asking some open questions‎.