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A lower bound for graph energy in terms of minimum and maximum degrees

Akbari, S ; Sharif University of Technology | 2021

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  1. Type of Document: Article
  2. Publisher: University of Kragujevac, Faculty of Science , 2021
  3. Abstract:
  4. The energy of a graph G, denoted by E(G), is defined as the sum of absolute values of all eigenvalues of G. In (MATCH Commun. Math. Comput. Chem. 83 (2020) 631{633) it was conjectured that for every graph G with maximum degree Δ(G) and minimum degree Δ (G) whose adjacency matrix is non-singular, E(G) +δ (G) + Δ (G) and the equality holds if and only if G is a complete graph. Here, we prove the validity of this conjecture for planar graphs, triangle-free graphs and quadrangle-free graphs. © 2021 University of Kragujevac, Faculty of Science. All rights reserved
  5. Keywords:
  7. Source: Match ; Volume 86, Issue 3 , 2021 , Pages 549-558 ; 03406253 (ISSN)
  8. URL: https://match.pmf.kg.ac.rs/electronic_versions/Match86/n3/match86n3_549-558.pdf