On 1-factors of point determining graphs

A graph G is said to be point determining if and only if distinct points of G have distinct neighborhoods. For such a graph G, the nucleus is defined to be the set G″ consisting of all points ν of G for which G-ν is a point determining graph.In 4], Summer exhibited several families of graphs H such that if G⁰ = H, for some point determining graph G, then G has a 1-factor. In this paper, we extend this class of graphs.