The average size of connected vertex subsets a graph generalises much-studied parameter for subtrees trees. For trees, the possible values this are critically affected by presence or absence vertices degree 2. We answer two questions Andrew Vince regarding effect constraints on general graphs. give new lower bound, and first non-trivial upper maximum growth rate number sets cubic graph, in fact...

Let o(G) be the average order of elements G, where G is a finite group. We show that there no polynomial lower bound for in terms o(N), N⊴G, even when prime-power group and N abelian. This gives negative answer to question A. Jaikin-Zapirain.