Let \(\varLambda (T)\) denote the set of leaves in a tree T. One natural problem is to look for spanning T given graph G such that as large possible. Recently, similar but stronger notion called robust connectivity was introduced, which defined minimum value \(\frac{|R \cap \varLambda (T)|}{|R|}\) taken over all nonempty subsets \({R\subseteq V(G)}\), where \(T = T(R)\) on chosen maximize \({|R...

The power graph of a group G is the graph whose vertex set is G and two distinct vertices are adjacent if one is a power of the other. In this paper, the minimum degree of power graphs of certain classes of cyclic groups, abelian p-groups, dihedral groups and dicyclic groups are obtained. It is ascertained that the edge-connectivity and minimum degree of power graphs are equal, and consequently...