Shahrood University of TechnologyJournal of Algebraic Systems2345-51288220210101NEW BOUNDS AND EXTREMAL GRAPHS FOR DISTANCE SIGNLESS LAPLACIAN SPECTRAL RADIUS231250195410.22044/jas.2020.9540.1469ENA.AlhevazFaculty of Mathematical Sciences, Shahrood University of Technology, P.O. Box:
316-3619995161, Shahrood, Iran.0000-0001-6167-607XM.BaghipurDepartment of Mathematics, University of Hormozgan, P.O. Box 3995, Bandar
Abbas, Iran.0000-0002-9069-9243S.PaulDepartment of Applied Sciences, Tezpur University, Tezpur-784028, India.Journal Article20200407The 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 paper, we determine some new upper and lower bounds on the distance signless Laplacian spectral radius of $G$ and characterize the extremal graphs attaining these bounds.https://jas.shahroodut.ac.ir/article_1954_3d76b11a1deafa958368655d5c44160b.pdf