Channel assignment on Cayley graphs
Patrick Bahls · Journal of Graph Theory · 2010
We address various channel assignment problems on the Cayley graphs of certain groups, computing the frequency spans by applying group theoretic techniques. In particular, we show that if G is the Cayley graph of an n-generated group Γ with a certain kind of presentation, then λ(G;k, 1)≤2(k+n−1). For certain values of k this bound gives the obvious optimal value for any 2n-regular graph. A large number of groups (for instance, even Artin groups and a number of Baumslag–Solitar groups) satisfy this condition. © 2010 Wiley Periodicals, Inc. J Graph Theory 67: 169-177, 2011