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Some results on spectrum and energy of graphs with loops

Akbari, S ; Sharif University of Technology | 2023

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  1. Type of Document: Article
  2. DOI: 10.1007/s40840-023-01489-z
  3. Publisher: Springer , 2023
  4. Abstract:
  5. Let GS be a graph with loops obtained from a graph G of order n and loops at S⊆ V(G). In this paper, we establish a neccesary and sufficient condition on the bipartititeness of a connected graph G and the spectrum Spec (GS) and Spec (GV(G)S). We also prove that for every S⊆ V(G) , E(GS) ≥ E(G) when G is bipartite. Moreover, we provide an identification of the spectrum of complete graphs Kn and complete bipartite graphs Km,n with loops. We characterize any graphs with loops of order n whose eigenvalues are all positive or non-negative, and also any graphs with a few distinct eigenvalues. Finally, we provide some bounds related to GS. © 2023, The Author(s), under exclusive licence to Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia
  6. Keywords:
  7. Energy ; Self-loop graphs ; Spectrum
  8. Source: Bulletin of the Malaysian Mathematical Sciences Society ; Volume 46, Issue 3 , 2023 ; 01266705 (ISSN)
  9. URL: https://link.springer.com/article/10.1007/s40840-023-01489-z