On the domination number and the total domination number of Fibonacci cubes

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SAYGI E.

ARS MATHEMATICA CONTEMPORANEA, cilt.16, sa.1, ss.245-255, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 16 Sayı: 1
  • Basım Tarihi: 2019
  • Doi Numarası: 10.26493/1855-3974.1591.92e
  • Dergi Adı: ARS MATHEMATICA CONTEMPORANEA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.245-255
  • Anahtar Kelimeler: Fibonacci cubes, domination number, total domination number, integer linear programming, DISJOINT HYPERCUBES, LUCAS
  • Hacettepe Üniversitesi Adresli: Evet

Özet

Fibonacci cubes are the special subgraphs of the hypercubes. Their domination numbers and total domination numbers are obtained for some small dimensions by integer linear programming. For larger dimensions upper and lower bounds on these numbers are given. In this paper, we present the up-down degree polynomials for Fibonacci cubes containing the degree information of all vertices in more detail. Using these polynomials we define optimization problems whose solutions give better lower bounds on the domination numbers and total domination numbers of Fibonacci cubes. Furthermore, we present better upper bounds on these numbers.