73 citations · 79 across the 4 of their papers we have counts for
4 papers
Growing scale-free simplices
K. Kovalenko, I. Sendiña-Nadal, N. Khalil +6
The past two decades have seen significant successes in our understanding of complex networked systems, from the mapping of real-world social, biological and technological networks…
Uniqueness of the extremal graph in the problem of maximizing the number of independent sets in regular graphs
Alexei Dmitriev, Alex Dainiak
The main purpose of this paper is to prove the uniqueness of a graph attaining the maximum of the number of independent sets over all -regular graphs on vertices for .
Inverse problems for the number of maximal independent sets
Alex Dainiak
We study the following inverse graph-theoretic problem: how many vertices should a graph have given that it has a specified value of some parameter. We obtain asymptotic for the mi…
Sharp bounds for the number of maximal independent sets in trees of fixed diameter
Alexander Dainiak
We obtain sharp lower and upper bounds for the number of maximal (under inclusion) independent sets in trees with fixed number of vertices and diameter. All extremal trees are desc…