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Improved lower bound on the energy of line graphs

Akbari, S ; Sharif University of Technology | 2023

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  1. Type of Document: Article
  2. DOI: 10.1016/j.laa.2023.05.023
  3. Publisher: Elsevier Inc , 2023
  4. Abstract:
  5. The energy of a graph is defined as the sum of absolute values of all eigenvalues of its adjacency matrix. For a nonempty graph G, S. Akbari, A. Alazemi, M. Andelić and M.A. Hosseinzadeh proposed a conjecture: The energy of the line graph of G is at least |E(G)|+Δ(G)−3, where E(G) is the edge set of G and Δ(G) is the maximum degree of G. In this paper, we give a proof confirming the conjecture, and present a lower bound and an upper bound for the energy of line graphs of regular graphs. © 2023 Elsevier Inc
  6. Keywords:
  7. Energy ; Line graph ; Maximum degree
  8. Source: Linear Algebra and Its Applications ; Volume 674 , 2023 , Pages 442-452 ; 00243795 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/abs/pii/S0024379523002069