# grinpy.invariants.dsi.sub_k_domination_number¶

grinpy.invariants.dsi.sub_k_domination_number(G, k)

Return the sub-k-domination number of the graph.

The sub-k-domination number of a graph G with n nodes is defined as the smallest positive integer t such that the following relation holds:

$t + \frac{1}{k}\sum_{i=0}^t d_i \geq n$

where

${d_1 \geq d_2 \geq \cdots \geq d_n}$

is the degree sequence of the graph.

Parameters: G (NetworkX graph) – An undirected graph. k (int) – A positive integer. The sub-k-domination number of a graph. int

Examples

>>> G = nx.cycle_graph(4)
>>> nx.sub_k_domination_number(G, 1)
True


References

D. Amos, J. Asplund, B. Brimkov and R. Davila, The sub-k-domination number of a graph with applications to k-domination, arXiv preprint arXiv:1611.02379, (2016)