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:

$t +$

rac{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.

G : graph
A Networkx graph.
k : int
A positive integer.
sub : int
The sub-k-domination number of a graph.

slater

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


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)