On the incidence coloring number of folded hypercubes

Let _Xi(G) denote the incidence coloring number of a graph G. An easy observation shows that _Xi(G) ≥ Δ(G) + 1, where Δ(G) is the maximum degree of G. In this paper, we study the problem of incidence coloring on folded hypercubes. Since the n-dimensional folded hypercube FQ_n contains n-dimensional hypercube Q_n as a subgraph, based on a technique of Hamming codes for Q_n, we acquire some results of X_i(FQ_n) as follows: (1) X_i(FQ_n) = n + 2 if n = 2^r - 2; (2) X_i(FQ_n) = n + 3 if n = 2^r - 1; and (3) Xi(FQ_n) ≥ n + 3 otherwise.