Name
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. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.23638/DMTCS-19-3-8 | DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE |
Keywords | DocType | Volume |
Circular separation dimension,planar graph,2-outerplanar graph,series-parallel graph | Journal | 19.0 |
Issue | ISSN | Citations |
3.0 | 1462-7264 | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Arpitha P. Bharathi | 1 | 0 | 0.34 |
| Minati De | 2 | 45 | 10.11 |
| Abhiruk Lahiri | 3 | 7 | 0.86 |