A graph G of order n (?2) is said to be panconnected if for each pair (x,y) of vertices of G there exists an xy-path of length ? for each ? such that d G (x,y)???n?1, where d G (x,y) denotes the length of a shortest xy-path in G. In this paper, we consider the panconnectivity of Cartesian product graphs. As a consequence of our results, we prove that the n-dimensional generalized hypercube Q n (k 1,k 2,?,k n ) is panconnected if and only if k i ?3 (i=1,?,n), which generalizes a result of Hsieh et al. that the 3-ary n-cube $Q^{3}_{n}$ is panconnected.
['You Lu', 'Jun-Ming Xu']
Panconnectivity of Cartesian product graphs