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Laplacian eigenvalue distribution and graph parameters

Ahanjideh, M ; Sharif University of Technology | 2022

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  1. Type of Document: Article
  2. DOI: 10.1016/j.laa.2021.09.012
  3. Publisher: Elsevier Inc , 2022
  4. Abstract:
  5. Let G be a graph and I be an interval. In this paper, we present bounds for the number mGI of Laplacian eigenvalues in I in terms of structural parameters of G. In particular, we show that mG(n−α(G),n]≤n−α(G) and mG(n−d(G)+3,n]≤n−d(G)−1, where α(G) and d(G) denote the independence number and the diameter of G, respectively. Also, we characterize bipartite graphs that satisfy mG[0,1)=α(G). Further, in the case of triangle-free or quadrangle-free, we prove that mG(n−1,n]≤1. © 2021 Elsevier Inc
  6. Keywords:
  7. Laplacian eigenvalue ; Graph theory ; Laplace transforms ; Bipartite graphs ; Distribution parameters ; Eigenvalues distribution ; Graph parameters ; Independence number ; Laplacian eigenvalues ; Structural parameter ; Triangle-free ; Eigenvalues and eigenfunctions
  8. Source: Linear Algebra and Its Applications ; Volume 632 , 2022 , Pages 1-14 ; 00243795 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/abs/pii/S0024379521003451