The Connected Hub Number and the Connected Domination Number

The connected hub number h(c)(G) of a connected graph G is the smallest order of a connected subgraph H of G such that any two nonadjacent vertices of G-H are joined in G by a path with all internal vertices in H. Letting gamma(c)(G) denote the connected domination number of G, it is easy to see that h(c)(G) <= gamma(c)(G) <= h(c)(G) + 1 for every connected graph G. Here we characterize the graphs G for which gamma(c)(G) = h(c)(G) + 1. Our result contributes to the search for the solution of an extremal problem of (Newman-Wolfe et al., Congressus Numerantium 67 (1988), 67-76). (C) 2011 Wiley Periodicals, Inc. NETWORKS, Vol. 58(3), 232-237 2011