Hamiltonian Laceability in Book Graphs

A connected graph network G is a Hamilton-t-laceable (Hamilton- t*-laceable) if Ǝ in G a Hamilton path connecting each pair (at least one pair) of vertices at distance ‘t’ in G such that 1 ≤ t ≤ diameter (G). In this paper, we discuss the f-edge-Hamilton-t-laceability of Book and stacked Book graphs, where 1 ≤ t ≤ diameter (G).

Edge Fault-Tolerant Strong Hamiltonian Laceability of Balanced Hypercubes

The balanced hypercube BHn, proposed by Wu and Huang, is a new variation of hypercube. A Hamiltonian bipartite graph is Hamiltonian laceable if there exists a Hamiltonian path between two arbitrary vertices from different partite sets. A Hamiltonian laceable graph G is strongly Hamiltonian laceable if there is a path of length [Formula: see text] between any two distinct vertices of the same partite set. A graph G is called k-edge-fault strong Hamiltonian laceable, if G – F is strong Hamiltonian laceable for any edge-fault set F with [Formula: see text]. It has been proved that the balanced hypercube BHn is strong Hamiltonian laceable. In this paper, we improve the above result and prove that BHn is (n – 1)-edge-fault strong Hamiltonian laceable.