## Functigraphs: an extension of permutation graphs.(English)Zbl 1224.05165

Summary: Let $$G_1$$ and $$G_2$$ be copies of a graph $$G$$, and let $$f\: V(G_1) \rightarrow V(G_2)$$ be a function. Then a functigraph $$C(G, f)=(V, E)$$ is a generalization of a permutation graph, where $$V=V(G_1) \cup V(G_2)$$ and $$E=E(G_1) \cup E(G_2)\cup \{uv\: u \in V(G_1), v \in V(G_2),v=f(u)\}$$. In this paper, we study colourability and planarity of functigraphs.

### MSC:

 05C15 Coloring of graphs and hypergraphs 05C10 Planar graphs; geometric and topological aspects of graph theory

### Keywords:

permutation graph; generalized Petersen graph; functigraph
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