Path-neighborhood graphs

Abstract

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 Pk -graph is a path-neighborhood graph in which every neighborhood is a Pk , where Pk is the path on k vertices. The Pk -graphs are characterized for k ≤ 4.