Traversing every edge in each direction once, but not at once: Cubic (polyhedral) graphs
| Main Author: | Rosenfeld, Vladimir R.; Department of Computer Science and Mathematics, Ariel University, Ariel 40700, Israel |
|---|---|
| Other Authors: | Ministry of Absorption of the State Israel (through fellowship “Shapiro”) |
| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB
, 2017
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| Subjects: | |
| Online Access: |
http://www.ejgta.org/index.php/ejgta/article/view/339 http://www.ejgta.org/index.php/ejgta/article/view/339/pdf_43 |
Daftar Isi:
- A {\em retracting-free bidirectional circuit} in a graph $G$ is a closed walk which traverses every edge exactly once in each direction and such that no edge is succeeded by the same edge in the opposite direction. Such a circuit revisits each vertex only in a number of steps. Studying the class $\mathit{\Omega}$ of all graphs admitting at least one retracting-free bidirectional circuit was proposed by Ore (1951) and is by now of practical use to nanotechnology. The latter needs in various molecular polyhedra that are constructed from a single chain molecule in the retracting-free way. Some earlier results for simple graphs, obtained by Thomassen and, then, by other authors, are specially refined by us for a cubic graph $Q$. Most of such refinements depend only on the number $n$ of vertices of $Q$.