Tadpole Graphs and Their Laceability

A connected graph G is termed Hamiltonian-t-laceable (t*-laceable) if there exists in G a Hamiltonian path between every pair (at least one pair) of its vertices u and v with the property d(u,v) = t. The Tadpole graph is the graph obtained by joining a cycle graph Cm to a path graph Pn with a bridge. In this paper, we discuss the laceability properties associated with the Tadpole graph