The Domination Number of On-line Social Networks and Random Geometric Graphs

Anthony Bonato (1) , Marc Lozier (1) , Dieter Mitsche (2) , Xavier Pérez-Giménez (3) , Pawel Pralat (3)

1 Department of Mathematics [Ryerson University - Toronto]
2 UNS - Université Nice Sophia Antipolis (1965 - 2019)
3 Ryerson University [Toronto]

We consider the domination number for on-line social networks, both in a stochastic network model, and for real-world, networked data. Asymptotic sublinear bounds are rigorously derived for the domination number of graphs generated by the memoryless geometric protean random graph model. We establish sublinear bounds for the domination number of graphs in the Facebook 100 data set, and these bounds are well-correlated with those predicted by the stochastic model. In addition, we derive the asymptotic value of the domination number in classical random geometric graphs.

Domaines: Combinatoire [math.CO]

Anthony Bonato, Marc Lozier, Dieter Mitsche, Xavier Pérez-Giménez, Pawel Pralat. The Domination Number of On-line Social Networks and Random Geometric Graphs. Proceedings of the 12th Conference on Theory and Applications of Models of Computation (TAMC 2015), May 2015, Singapour, Singapore. pp.14, ⟨10.1007/978-3-319-17142-5_14⟩. ⟨hal-01291967⟩