L (p, q)-labelling of K-4-minor free graphs
For positive integers p and q, an L(p, q)-labelling of a graph G is a function phi from the vertex set V(G) to the integer set (0, 1,... k) such that vertical bar phi(x) - phi(y)vertical bar > p if x and y are adjacent and vertical bar phi(x) - phi(y)vertical bar >, q if x and y are at distance 2. The L(p, q)-labelling number lambda(G p, q) of G is the smallest k such that G has an L(p, q)-labelling with max {phi(v) vertical bar v is an element of V(G)} = k. In this paper we prove that, if p + q >= 3 and G is a K-4-minor free graph with maximum degree Delta, then lambda(G; p, q)  = 4. (c) 2006 Elsevier B.V. All rights reserved.
l (p,q)-labelling k-4-minor free graph distance channel assignment