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论文类型：期刊论文

发表时间：2008-01-01

发表刊物：ARS COMBINATORIA

收录刊物：SCIE

卷号：86

页面范围：23-31

ISSN号：0381-7032

关键字：(a, d)-antimagic labeling; Petersen graph; vertex labeling; edge labeling

摘要：A connected graph G = (V, E) is said to be (a, d)-antimagic if there exist positive integers a, d and a bijection f : E -> {1, 2,..., vertical bar E vertical bar} such that the induced mapping g(f) : V -> N, defined by g(f)(v) = Sigma f (uv), uv is an element of E(G), is injective and g(f)(V)={a,a + d,...,a + (vertical bar V vertical bar-1)d}. Mirka Miller and Martin Baca proved that the generalized Petersen graph P(n,2) is (3n+6/2, 3)-antimagic for n equivalent to 0(mod 4), n >= 8 and conjectured that the generalized Petersen graph P(n, k) is (3n+6/2, 3)antimagic for even n and 2 <= k <= n/2-1. In this paper, we show that the generalized Petersen graph P(n, 3) is (3n+6/2, 3)antimagic for even n >= 8.