Objects, Invariants and Properties for Graph Theory (GT) automated conjecturing: in particular with the Sage program CONJECTURING: http://nvcleemp.github.io/conjecturing/
from:
Loh, Po-Shen, and Jie Ma. "Diameter critical graphs." Journal of Combinatorial Theory, Series B 117 (2016): 34-58.
returned graph is guaranteed to be diameter-2-critical
compare Issues #631 and #632
add this in AUXILIARY FUNCTIONS
def diameter_2_critical_generator(g): #g and g_complement must be no more than diameter 2
if not g.is_connected() or g.diameter() > 2:
return None
gc = g.complement()
if not gc.is_connected() or gc.diameter() > 2:
return None
h = g.disjoint_union(gc)
n = g.order()
for v in g.vertices():
h.add_edge((0,v),(1,v))
h.relabel()
return h
from: Loh, Po-Shen, and Jie Ma. "Diameter critical graphs." Journal of Combinatorial Theory, Series B 117 (2016): 34-58.
returned graph is guaranteed to be diameter-2-critical
compare Issues #631 and #632
add this in AUXILIARY FUNCTIONS
def diameter_2_critical_generator(g): #g and g_complement must be no more than diameter 2
if not g.is_connected() or g.diameter() > 2: return None gc = g.complement()