Horadam-Lucas Cubes

Tan E., Podrug L., Chenoweth V. I.

AXIOMS, sa.12, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2024
  • Doi Numarası: 10.3390/axioms13120837
  • Dergi Adı: AXIOMS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED)
  • Ankara Üniversitesi Adresli: Evet

Özet

In this paper, we introduce a novel class of graphs referred to as the Horadam-Lucas cubes. This class extends the concept of Lucas cubes and retains numerous desirable properties associated with them. Horadam-Lucas cubes can also be viewed as a companion graph family of the Horadam cubes, in a similar way the Lucas cubes relate to Fibonacci cubes or the Lucas-run graphs relate to Fibonacci-run graphs. As special cases, they also give rise to new graph families, such as Pell-Lucas cubes and Jacobsthal-Lucas cubes. We derive the several metric and enumerative properties of these cubes, including their diameter, periphery, radius, fundamental decomposition, number of edges, cube polynomials, and generating function of the cube polynomials.