Ordering of minimal energies in unicyclic signed graphs

• Tahir Shamsher ^[1] ; Mushtaq A. Bhat ^[3] ; Shariefuddin Pirzada ^[1] ; Yilun Shang ^[2]
  1. [1] University of Kashmir

     University of Kashmir

     India

     
  2. [2] Northumbria University

     Northumbria University

     Reino Unido

     
  3. [3] National Institute of Technology, India

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• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 65, Nº. 1, 2023, págs. 119-133
• Idioma: inglés
• DOI: 10.33044/revuma.2565
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• Resumen

  • Let S = (G, σ) be a signed graph of order n and size m and let t P1, t2, . . . , tn be the eigenvalues of S. The energy of S is defined as E(S) =nj=1 |tj |. A connected signed graph is said to be unicyclic if its order and size are the same. In this paper we characterize, up to switching, the unicyclic signed graphs with first 11 minimal energies for all n ≥ 11. For 3 ≤ n ≤ 7, we provide complete orderings of unicyclic signed graphs with respect to energy. For 8 ≤ n ≤ 10, we determine unicyclic signed graphs with first 13 minimal energies.