The Stober-Weißgraphs are the family of geodetic graphs 
constructed by Stober and Weiß (2026), where 
and 
are integers.
First construct a graph 
. Take disjoint complete
graphs 
and 
,
with vertices 
and 
, and 
disjoint copies of a star graph
with 
tree leaves. Write 
for the graph center and
for tree leaf 
of star graph 
. Join 
to 
, and 
to 
, by internally vertex-disjoint paths
of path length 
. These paths are otherwise
disjoint from the cliques and star
graphs. This is the Bosák graph 
(Bosák 1978).
Now take 
,
,
and 
.
Identify the 
in the first copy with the corresponding 
in the second, identify the two corresponding 
cliques, and identify the two
corresponding 
cliques. The resulting graph is
.
It has
 |
vertices, is geodetic, and has graph diameter 
.
The smallest member 
has 24 vertices,
graph diameter 4, and was the first member found
in the computer search that led to the general construction (Stober and Weiß
2026).
