The bondage number 
of a finite simple graph 
with at least one graph
edge is the minimum number of graph
edges whose deletion increases its domination
number (Fink et al. 1990). Writing 
for the edge set and 
for the domination
number,
 |
where 
is obtained by edge deletion of every graph
edge in 
,
retaining all graph vertices.
For the truncated octahedral graph 
, Srivastava (2026) proved that 
and 
. Since 
is planar and cubic,
this refutes the planar bondage conjecture,
which proposed the bound 
, where 
is the maximum
vertex degree. Srivastava (2026) reports using OpenAI Codex for search-code development
and independent-check design.
