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.

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doi.org/10.7151/dmgt.1700, hdl.handle.net/1765/74902
Discussiones Mathematicae - Graph Theory
Erasmus School of Economics

Laskar, R. C., & Mulder, M. (2013). Path-neighborhood graphs. Discussiones Mathematicae - Graph Theory, 33(4), 731–745. doi:10.7151/dmgt.1700