On the planarity of some transformation graphs. (Chinese. English summary) Zbl 1150.05378
Summary: Let \(G\) be a simple graph, \(G^{--+}, G^{-+-}\) are the transformation graphs of \(G\). In this paper, it is shown that for a graph \(G\),
- (1)
- \(G^{--+}\) is planar if and only if \(n\leq 3\) or \(G\) is isomorphic to one of the following graphs: \(2K_1+K_2, K_1+K_{1, 3}\) or \(K_1+C_3\);
- (2)
- \(G^{-+-}\) is planar if \(n\leq 4\) and \(G\) only if and is not isomorphic to \(K_4-e\).
MSC:
| 05C60 | Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) |
