## Tiziana Calamoneri ; Angelo Monti ; Blerina Sinaimeri - On the domination number of $t$-constrained de Bruijn graphs

dmtcs:8879 - Discrete Mathematics & Theoretical Computer Science, August 22, 2022, vol. 24, no 2 - https://doi.org/10.46298/dmtcs.8879
On the domination number of $t$-constrained de Bruijn graphs

Authors: Tiziana Calamoneri ; Angelo Monti ; Blerina Sinaimeri

Motivated by the work on the domination number of directed de Bruijn graphs and some of its generalizations, in this paper we introduce a natural generalization of de Bruijn graphs (directed and undirected), namely $t$-constrained de Bruijn graphs, where $t$ is a positive integer, and then study the domination number of these graphs. Within the definition of $t$-constrained de Bruijn graphs, de Bruijn and Kautz graphs correspond to 1-constrained and 2-constrained de Bruijn graphs, respectively. This generalization inherits many structural properties of de Bruijn graphs and may have similar applications in interconnection networks or bioinformatics. We establish upper and lower bounds for the domination number on $t$-constrained de Bruijn graphs both in the directed and in the undirected case. These bounds are often very close and in some cases we are able to find the exact value.

Volume: vol. 24, no 2
Section: Graph Theory
Published on: August 22, 2022
Accepted on: July 5, 2022
Submitted on: December 21, 2021
Keywords: Mathematics - Combinatorics,05Cxx, 05C69