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Path-Neighborhood Graphs

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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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  • Department of Mathematical Sciences, Clemson University Clemson, SC 29634, USA
  • Econometrisch Instituut, Erasmus Universiteit P.O. Box 1738, 3000 DR Rotterdam, The Netherlands


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