Quasi-Laplacian energy of fractal graphs

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BERBERLER M. E.

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

• 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.