A Note on Energy and Sombor Energy of Graphs

Bilal Ahmad Rather, Muhammad Imran

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


For a graph G with V (G) = {v1, v2, ..., vn} and degree sequence (dv1, dv2, ..., dvn), the adjacency matrix A(G) of G is a (0, 1) square matrix of order n with ij-th entry 1, if vi is adjacent to vj and 0, otherwise. The Sombor matrix S(G) = (sij) is a square matrix of order n, where sij = ∑d2vi + d2vj, whenever vi is adjacent to vj, and 0, otherwise. The sum of the absolute values of the eigenvalues of A(G) is the energy, while the sum of the absolute eigenvalues of S(G) is the Sombor energy of G. In this note, we provide counter examples to the upper bound of Theorem 18 in [13] and Theorem 1 in [16].

Original languageEnglish
Pages (from-to)467-477
Number of pages11
Issue number2
Publication statusPublished - 2023

ASJC Scopus subject areas

  • General Chemistry
  • Computer Science Applications
  • Computational Theory and Mathematics
  • Applied Mathematics


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