A Generalization of Dirac's Theorem for K(1,3)-free Graphs

It is known that ff a 2-connected graph G of suiBciently large order n satisfies the property that the union of the neighborhoods of each pair of vertices has cardinallty at least ~-, " then G is hamiltonian. In this paper, we obtain a similar generalization of Dirac's Theorem for K(1, 3)-free graphs. In particular, we show that if G is a 2-connected K(1, 3)-free graph of order n with the cardinality of the union of the neighborhoods of each pair of vertices at least (,+1) then G is hamiltonian. 3 ' We also investigate several other related properties in K(1, 3)-free graphs such as traceability, hamiltonian-connectedness, and pancyclicity.