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

Elif Saygı

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.

Keywords


Fibonacci cubes, domination number, total domination number, integer linear programming

Full Text:

PDF


DOI: https://doi.org/10.26493/1855-3974.1591.92e

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications