Path-neigborhood graphs
Renu C. Laskar, Henry Martyn Mulder · Discussiones Mathematicae Graph Theory · 2013
A path-neighborhood graph is a connected graph in which every neighborhood induces a path.In the main results the 3-sun-free path-neighborhood graphs are characterized.The 3-sun is obtained from a 6-cycle by adding three chords between the three pairs of vertices at distance 2. A P k -graph is a path-neighborhood graph in which every neighborhood is a P k , where P k is the path on k vertices.The P k -graphs are characterized for k ≤ 4.