Bounds for the Generalized Distance Eigenvalues of a Graph

Abdollah Alhevaz, Maryam Baghipur, Hilal Ahmad Ganie, Yilun Shang

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)
45 Downloads (Pure)


Let G be a simple undirected graph containing n vertices. Assume G is connected. Let D ( G ) be the distance matrix, D L ( G ) be the distance Laplacian, D Q ( G ) be the distance signless Laplacian, and T r ( G ) be the diagonal matrix of the vertex transmissions, respectively. Furthermore, we denote by D α ( G ) the generalized distance matrix, i.e., D α ( G ) = α T r ( G ) + ( 1 - α ) D ( G ) , where α ∈ [ 0 , 1 ] . In this paper, we establish some new sharp bounds for the generalized distance spectral radius of G, making use of some graph parameters like the order n, the diameter, the minimum degree, the second minimum degree, the transmission degree, the second transmission degree and the parameter α , improving some bounds recently given in the literature. We also characterize the extremal graphs attaining these bounds. As an special cases of our results, we will be able to cover some of the bounds recently given in the literature for the case of distance matrix and distance signless Laplacian matrix. We also obtain new bounds for the k-th generalized distance eigenvalue.
Original languageEnglish
Article number1529
Issue number12
Publication statusPublished - 17 Dec 2019


Dive into the research topics of 'Bounds for the Generalized Distance Eigenvalues of a Graph'. Together they form a unique fingerprint.

Cite this