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Upper bounds on the energy of graphs in terms of matching number

Akbari, S ; Sharif University of Technology | 2021

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  1. Type of Document: Article
  2. DOI: 10.2298/AADM201227016A
  3. Publisher: University of Belgrade , 2021
  4. Abstract:
  5. The energy of a graph G, ϵ(G), is the sum of absolute values of the eigenvalues of its adjacency matrix. The matching number µ(G) is the number of edges in a maximum matching. In this paper, for a connected graph G of order n with largest vertex degree ∆ ≥ 6 we present two new upper bounds for the energy of a graph: (Formula presented) and (Formula presented). The latter one improves recently obtained bound (Formula presented) where ∆e stands for the largest edge degree and a = 2(∆e + 1). We also present a short proof of this result and several open problems. © 2021
  6. Keywords:
  7. Energy (of graph) ; Matching number ; Graph energy
  8. Source: Applicable Analysis and Discrete Mathematics ; Volume 15, Issue 2 , 2021 , Pages 444-459 ; 14528630 (ISSN)
  9. URL: http://www.doiserbia.nb.rs/Article.aspx?ID=1452-86302100016A