Geodesic
Functigraphs: An extension of permutation graphs
Mathematica Bohemica, Tome 136 (2011) no. 1, pp. 27-37.

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Let $G_1$ and $G_2$ be copies of a graph $G$, and let $f\colon V(G_1) \rightarrow V(G_2)$ 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 $E=E(G_1) \cup E(G_2)\cup \{uv \colon u \in V(G_1), v \in V(G_2),v=f(u)\}$. In this paper, we study colorability and planarity of functigraphs.
DOI : 10.21136/MB.2011.141447
Classification : 05C10, 05C15
Keywords: permutation graph; generalized Petersen graph; functigraph 
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Chen, Andrew; Ferrero, Daniela; Gera, Ralucca; Yi, Eunjeong. Functigraphs: An extension of permutation graphs. Mathematica Bohemica, Tome 136 (2011) no. 1, pp. 27-37. doi : 10.21136/MB.2011.141447. http://geodesic.mathdoc.fr/articles/10.21136/MB.2011.141447/

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