Results on the domination number and the total domination number of Lucas cubes
Abstract
Lucas cubes are the special subgraphs of Fibonacci cubes. For small dimensions, their domination numbers are obtained by direct search or integer linear programming. For larger dimensions some bounds on these numbers are given. In this work, we present the exact values of total domination number of small dimensional Lucas cubes and present optimization problems obtained from the degree information of Lucas cubes, whose solutions give better lower bounds on the domination numbers and total domination numbers of Lucas cubes.
Keywords
Lucas cube, Fibonacci cube, domination number, total domination number, integer linear programming
DOI: https://doi.org/10.26493/1855-3974.2028.cb4
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