On distance signless Laplacian spectrum and energy of graphs

Abdollah Alhevaz, Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran, Maryam Baghipur, Ebrahim Hashemi, Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran
2018 Electronic Journal of Graph Theory and Applications  
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 is the distance matrix of G and T r(G) is the diagonal matrix of vertex transmissions of G. In this paper, we determine some upper and lower bounds on the distance signless Laplacian spectral radius of G based on its order and independence number, and characterize the extremal graphs. In addition, we give an exact description of the distance
more » ... signless Laplacian spectrum and the distance signless Laplacian energy of the join of regular graphs in terms of their adjacency spectrum.
doi:10.5614/ejgta.2018.6.2.12 fatcat:3yg27dw6wffvjjx3isugqid7la