On the incidence coloring number of folded hypercubes
Kung-Jui Pai, Jou–Ming Chang, Jinn‐Shyong Yang, Ro–Yu Wu · 2014
LetXi(G) denote the incidence coloring number of a graph G. An easy observation shows thatXi(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 FQncontains n-dimensional hypercube Qnas a subgraph, based on a technique of Hamming codes for Qn, we acquire some results of Xi(FQn) as follows: (1) Xi(FQn) = n + 2 if n = 2r- 2; (2) Xi(FQn) = n + 3 if n = 2r- 1; and (3) Xi(FQn) ≥ n + 3 otherwise.