Open Problems

Let G be a connected graph. The subgraph number f_G(v) of a vertex v in G is the number of connected subgraphs of G containing the vertex v.  The subgraph core of G denoted by S_c(G) is the set of vertices with the maximum subgraph number in G. The follwing is a conjecture in this paper.

Conjecture: The subgraph core of a connected graph is either a cut vertex or lies in a block.