The effects of distance and neighborhood union conditions on hamiltonian properties in graphs
Terri Lindquester · Journal of Graph Theory · 1989
Abstract We prove that a 2‐connected graph G of order p is hamiltonian if for all distinct vertices u and v, dist(u,v) = 2 implies that |N(u) U N(v)| ⩾ (2p ‐ 1)/3. We also demonstrate hamiltonian‐connected and traceability properties in graphs under similar conditions.