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@oneman
Created February 5, 2026 05:39
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Letter,Connectedness,Components,Holes,Contractible,Simply Connected,Branching structure,Endpoints,Graph model,Euler characteristic,Genus
a,Connected and path-connected,1,1,No,No,One branch point of valence 3,1,Circle with attached tail (tree attached to loop),0,1
b,Connected and path-connected,1,1,No,No,One branch point of valence 3,1,Circle with attached tail,0,1
c,Connected and path-connected,1,0,Yes,Yes,None,2,Interval (simple arc),1,0
d,Connected and path-connected,1,1,No,No,One branch point of valence 3,1,Circle with attached tail,0,1
e,Connected and path-connected,1,0,Yes,Yes,One branch point of valence 3,3,"Y-shape (star graph K_{1,3})",1,0
f,Connected and path-connected,1,0,Yes,Yes,One branch point of valence 3,3,"Y-shape (star graph K_{1,3})",1,0
g,Connected and path-connected,1,2,No,No,One branch point of valence 4,0,Two circles wedged at a point (figure-8 curve),-1,2
h,Connected and path-connected,1,0,Yes,Yes,None,2,Interval,1,0
i,Not connected,2 (stem + dot),0,Yes (each component),Yes (each),None,"2 (stem), 0 (dot, assuming point-like)",Interval + point,2,0
j,Not connected,2 (hook + dot),0,Yes (each),Yes (each),None,"2 (hook), 0 (dot)",Interval + point,2,0
k,Connected and path-connected,1,0,Yes,Yes,Two branch points of valence 3,4,Line with two side branches,1,0
l,Connected and path-connected,1,0,Yes,Yes,None,2,Interval,1,0
m,Connected and path-connected,1,0,Yes,Yes,None,2,Interval,1,0
n,Connected and path-connected,1,0,Yes,Yes,None,2,Interval,1,0
o,Connected and path-connected,1,1,No,No,None,0,Circle,0,1
p,Connected and path-connected,1,1,No,No,One branch point of valence 3,1,Circle with attached tail,0,1
q,Connected and path-connected,1,1,No,No,One branch point of valence 3,1,Circle with attached tail,0,1
r,Connected and path-connected,1,0,Yes,Yes,None,2,Interval,1,0
s,Connected and path-connected,1,0,Yes,Yes,None,2,Interval,1,0
t,Connected and path-connected,1,0,Yes,Yes,One branch point of valence 4,4,"Star graph K_{1,4} (tree)",1,0
u,Connected and path-connected,1,0,Yes,Yes,None,2,Interval,1,0
v,Connected and path-connected,1,0,Yes,Yes,None,2,Interval,1,0
w,Connected and path-connected,1,0,Yes,Yes,None,2,Interval,1,0
y,Connected and path-connected,1,0,Yes,Yes,One branch point of valence 3,3,"Y-shape (star graph K_{1,3})",1,0
z,Connected and path-connected,1,0,Yes,Yes,None,2,Interval,1,0
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