QA528 : On distance signless Laplacian spectrum of graphs
Thesis > Central Library of Shahrood University > Mathematical Sciences > PhD > 2019
Authors:
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.
Keywords:
#Distance signless Laplacian matrix #distance signless Laplacian spectrum #spectral radius #distance signless Laplacian energy Link
Keeping place: Central Library of Shahrood University
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Keeping place: Central Library of Shahrood University
Visitor: