Pancyclicity and extendability in strong products
S. Ramachandran, R. Parvathy · Journal of Graph Theory · 1996
In this paper, we first prove that for any connected graph G with at least two vertices, there is an integer m for which the strong product X⌅Gm has pancyclic ordering from each vertex. After characterizing the graphs G for which GX⌅K2 is Hamiltonian, we determine a criterion for extendability of cycles. We also prove that if G is a connected, K1.3-free graph with δ ≥ 2, then GX⌅XK2 is fully cycle extendable as well as 1-edge Hamiltonian. © 1996 John Wiley & Sons, Inc.