A novel algebraic technique for adjacency matrices of some derived graphs

ÖZDEN AYNA H., YURTTAŞ GÜNEŞ A., Delen S., Huilgol M. I., Ozmen B., CANGÜL İ. N.

Mathematical and Computer Modelling of Dynamical Systems, cilt.31, sa.1, 2025 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 31 Sayı: 1
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1080/13873954.2025.2535726
  • Dergi Adı: Mathematical and Computer Modelling of Dynamical Systems
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, INSPEC, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Anahtar Kelimeler: Adjacency matrix, derived graph, line graph
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

Graph energy has been the main concern of spectral graph theory in the last five decades. The classical graph energy is the sum of the absolute values of the eigenvalues of the adjacency matrix. In many research papers, different versions of graph energy by utilizing different graph matrices are introduced. For many graph types corresponding to molecular structures, the energy is determined. The theory is complete for complete bipartite graphs. For derived graphs, the problem was settled partially for line, total, double and subdivision graphs. In this paper, the more complex cases of power graphs, shadow, image and core graphs are discussed, and the adjacency matrices of these derived graph classes are formed in terms of very simple submatrices.