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

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SAYGI E.

ARS MATHEMATICA CONTEMPORANEA, vol.16, no.1, pp.245-255, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 16 Issue: 1
  • Publication Date: 2019
  • Doi Number: 10.26493/1855-3974.1591.92e
  • Journal Name: ARS MATHEMATICA CONTEMPORANEA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.245-255
  • Keywords: Fibonacci cubes, domination number, total domination number, integer linear programming, DISJOINT HYPERCUBES, LUCAS
  • Hacettepe University Affiliated: Yes

Abstract

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.