The generalized 3-connectivity of burnt pancake graphs and godan graphs

The generalized k-connectivity of a graph G, denoted by kappa(k) (G), is the minimum number of internally edge disjoint S-trees for any S subset of V (G) and |S| = k: The generalized k-connectivity is a natural extension of the classical connectivity and plays a key role in applications related to the modern interconnection networks. The burnt pancake graph BPn and the godan graph EAn are two kinds of Cayley graphs which posses many desirable properties. In this paper, we investigate the generalized 3-connectivity of BPn and EA(n). We show that kappa(3) (BPn) = n 1 where n >= 2 and kappa(3)(EA(n)) = n- 1 where n >= 3.