科研之友
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摘要
Fora given graph G of order n, a k-L(2, 1)-labelling is defined as a function f : V(G) --> {0, 1, 2,... k) such that vertical bar f (u)-f (v)vertical bar >= 2 when d(G) (u, v) = 1 and vertical bar f (u) - f (v)vertical bar >= 1 when d(G) (u, v) = 2. The L(2, 1)-labelling number of G, denoted by lambda(G), is the smallest number k such that G has a k-L(2, I)-labelling. The hole index p(G) of G is the minimum number of integers not used in a;.(G)L(2, I)-labelling of G. We say G is full-colorable if p(G) = 0; otherwise, it will be called non-full colorable. In this paper, we consider the graphs with lambda(G) = 2m and rho(G) = m, where m is a positive integer. Our main work generalized a result by Fishburn and Roberts [No-hole L (2, 1)-colorings, Discrete Appl. Math. 130 (2003) 513-519].
