Quasi-Laplacian energy of fractal graphs
Acta et Commentationes Universitatis Tartuensis de Mathematica, cilt.28, sa.1, ss.5-18, 2024 (ESCI, Scopus)
- 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: Quasi-Laplacian matrix, quasi-Laplacian energy, Zagreb index, fractal graph, R-join, R-corona
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- 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.