# grinpy.invariants.dsi.sub_total_domination_number¶

grinpy.invariants.dsi.sub_total_domination_number(G)

Return the sub-total domination number of the graph.

The sub-total domination number is defined as:

$sub_{t}(G) = \min\{t : \sum_{i=0}^t d_i \geq n\}$

where

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

is the degree sequence of the graph ordered in non-increasing order and n is the order of the graph.

This invariant was defined and investigated by Randy Davila.

Parameters: G (NetworkX graph) – An undirected graph. The sub-total domination number of the graph. int

References

R. Davila, A note on sub-total domination in graphs. arXiv preprint arXiv:1701.07811, (2017)