Discussiones Mathematicae Graph Theory 33(4) (2013) 731-745
doi: 10.7151/dmgt.1700

[BIBTex] [PDF] [PS]

Path-neighborhood Graphs

R.C. Laskar

Department of Mathematical Sciences, Clemson University
Clemson, SC 29634, USA

Henry Martyn Mulder

Econometrisch Instituut, Erasmus Universiteit
P.O. Box 1738, 3000 DR Rotterdam, The Netherlands

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.

Keywords: path-neighborhood graph, outerplanar graph, MOP, snake, 3-sun, k-fun

2010 Mathematics Subject Classification: 05C75, 05C38, 05C99, 05C10.

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Received 28 November 2011
Revised 29 August 2012
Accepted 10 September 2012