grinpy.invariants.dsi.sub_k_domination_number¶
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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.
Returns: The sub-k-domination number of a graph.
Return type: int
See also
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)