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

Fibonacci cubes are special subgraphs of the hypercube graphs. 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.

• Publication year

  2019

• Venue

  Ars Math. Contemp.

• Publication date

  2019-01-04

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.26493/1855-3974.1591.92E
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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