Generalized Pell graphs

Iršıč V., Klavžar S., Tan E.

Turkish Journal of Mathematics, vol.47, no.7, pp.1955-1973, 2023 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 47 Issue: 7
  • Publication Date: 2023
  • Doi Number: 10.55730/1300-0098.3475
  • Journal Name: Turkish Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.1955-1973
  • Keywords: center of graph, Fibonacci cube, generating function, k-Fibonacci Sequence, median graph, Pell graph
  • Ankara University Affiliated: Yes

Abstract

In this paper, generalized Pell graphs Πn,k, k ≥ 2, are introduced. The special case of k = 2 are the Pell graphs Πn defined earlier by Munarini. Several metric, enumerative, and structural properties of these graphs are established. The generating function of the number of edges of Πn,k and the generating function of its cube polynomial are determined. The center of Πn,k is explicitly described; if k is even, then it induces the Fibonacci cube Γn. It is also shown that Πn,k is a median graph, and that Πn,k embeds into a Fibonacci cube.