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A short proof for graph energy is at least twice of minimum degree

Akbari, S ; Sharif University of Technology | 2020

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  1. Type of Document: Article
  2. Publisher: University of Kragujevac, Faculty of Science , 2020
  3. Abstract:
  4. The energy ϵ(G) of a graph G is the sum of the absolute values of all eigenvalues of G. Zhou in (MATCH Commun. Math. Comput. Chem. 55 (2006) 91-94) studied the problem of bounding the graph energy in terms of the minimum degree together with other parameters. He proved his result for quadrangle-free graphs. Recently, in (MATCH Commun. Math. Comput. Chem. 81 (2019) 393-404) it is shown that for every graph G, ϵ(G) ≥ 2δ(G), where δ(G) is the minimum degree of G, and the equality holds if and only if G is a complete multipartite graph with equal size of parts. Here, we provide a short proof for this result. Also, we give an affirmative answer to a problem proposed in (MATCH Commun. Math. Comput. Chem. 81 (2019) 393-404). © 2020 University of Kragujevac, Faculty of Science. All rights reserved
  5. Keywords:
  7. Source: Match ; Volume 83, Issue 3 , 2020 , Pages 631-633
  8. URL: https://match.pmf.kg.ac.rs/electronic_versions/Match83/n3/match83n3_631-633.pdf