Functigraphs: An extension of permutation graphs
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Let G1 and G2 be copies of a graph G, and let f:V (G1) V (G2) be a function. Then a functigraph C(G, f) = (V,E) is a generalization of a permutation graph, where V = V (G1) {n-ary union} V (G2) and E = E(G1) {n-ary union} E(G2) {n-ary union} {uv:u V (G1), v V (G2), v = f(u)}. In this paper, we study colorability and planarity of functigraphs.