Bharathi, Arpitha P and De, Minati and Lahiri, Abhiruk
(2017)
*Circular Separation Dimension of a Subclass of Planar Graphs.*
In: DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE, 19
(3).

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## Abstract

A pair of non-adjacent edges is said to be separated in a circular ordering of vertices, if the endpoints of the two edges do not alternate in the ordering. The circular separation dimension of a graph G, denoted by pi degrees (G), is the minimum number of circular orderings of the vertices of G such that every pair of non-adjacent edges is separated in at least one of the circular orderings. This notion is introduced by Loeb and West in their recent paper. In this article, we consider two subclasses of planar graphs, namely 2-outerplanar graphs and series-parallel graphs. A 2-outerplanar graph has a planar embedding such that the subgraph obtained by removal of the vertices of the exterior face is outerplanar. We prove that if G is 2-outerplanar then pi degrees (G) = 2. We also prove that if G is a series-parallel graph then pi degrees (G) <= 2.

Item Type: | Journal Article |
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Publication: | DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE |

Additional Information: | Copy right for the this article belong to the DISCRETE MATHEMATICS THEORETICAL COMPUTER SCIENCE, 62 RUE DU CARDINAL MATHIEU, F-54000 NANCY, FRANCE |

Department/Centre: | Division of Electrical Sciences > Computer Science & Automation |

Date Deposited: | 02 Mar 2018 14:55 |

Last Modified: | 02 Mar 2018 14:55 |

URI: | http://eprints.iisc.ac.in/id/eprint/59065 |

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