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.
@article{bwmeta1.element.doi-10_7151_dmgt_1700,
author = {R.C. Laskar and Henry Martyn Mulder},
title = {Path-Neighborhood Graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {33},
year = {2013},
pages = {731-745},
zbl = {1295.05195},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1700}
}
R.C. Laskar; Henry Martyn Mulder. Path-Neighborhood Graphs. Discussiones Mathematicae Graph Theory, Tome 33 (2013) pp. 731-745. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1700/
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