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.