Quasi-Laplacian energy of fractal graphs

Creative Commons License

BERBERLER M. E.

Acta et Commentationes Universitatis Tartuensis de Mathematica, cilt.28, sa.1, ss.5-18, 2024 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 28 Sayı: 1
  • Basım Tarihi: 2024
  • Doi Numarası: 10.12697/acutm.2024.28.01
  • Dergi Adı: Acta et Commentationes Universitatis Tartuensis de Mathematica
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier
  • Sayfa Sayıları: ss.5-18
  • Anahtar Kelimeler: fractal graph, quasi-Laplacian energy, Quasi-Laplacian matrix, R-corona, R-join, Zagreb index
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

Graph energy is a measurement of determining the struc-tural information content of graphs. The first Zagreb index can be han-dled with its connection to graph energy. In this paper, a novel and sig-nificant application of the first Zagreb index to composite graphs based on fractal graphs is revealed, and by the relation between quasi-Laplacian energy and the vertex degrees of a graph, we derive closed-form formu-las for the quasi-Laplacian energy of fractal graphs or namely R-graphs, R-vertex and edge join, R-vertex and edge corona, R-vertex and edge neighborhood graphs in terms of the corresponding energy, the first Zagreb indices, number of vertices and edges of the underlying graphs.