1 research outputs found
On extremal graphs with exactly one Steiner tree connecting any vertices
The problem of determining the largest number of
edges for graphs with vertices and maximal local connectivity at most
was considered by Bollob\'{a}s. Li et al. studied the largest number
of edges for graphs with vertices and at most
two internally disjoint Steiner trees connecting any three vertices. In this
paper, we further study the largest number of edges for
graphs with vertices and exactly one Steiner tree connecting any
vertices with . It turns out that this is not an easy task to finish,
not like the same problem for the classical connectivity parameter. We
determine the exact values of for ,
respectively, and characterize the graphs which attain each of these values.Comment: 11 page