Some results on one type of graph family with some special number sequences

Kirklar E., Maden A. D., YILMAZ F.

AKCE International Journal of Graphs and Combinatorics, vol.17, no.3, pp.749-754, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 17 Issue: 3
  • Publication Date: 2020
  • Doi Number: 10.1016/j.akcej.2019.09.005
  • Journal Name: AKCE International Journal of Graphs and Combinatorics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Emerging Sources Citation Index (ESCI), Scopus, zbMATH, Directory of Open Access Journals
  • Page Numbers: pp.749-754
  • Keywords: Hafnian, eigenvalue, energy, Fibonacci number, Pell number
  • Ankara Haci Bayram Veli University Affiliated: No

Abstract

© 2020 The Author(s). Published with license by Taylor & Francis Group, LLC.In this study, we introduce a new graph family. Then, we calculate eigenvalues of the adjacency and the Laplacian matrix of this graph family. Moreover, we show that the perfect matching number of this graph family equals to special second order recurrence by hafnian method. For some special kinds of this family, we obtain that the perfect matching number of corresponding graphs equals to some famous number sequences such as Fibonacci, Pell and Jacobsthal numbers. Also, we find energies and obtain upper bounds for Laplacian energies of these graphs.