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Indexed by:期刊论文

Date of Publication:2008-01-01

Journal:ARS COMBINATORIA

Included Journals:SCIE

Volume:86

Page Number:23-31

ISSN No.:0381-7032

Key Words:(a, d)-antimagic labeling; Petersen graph; vertex labeling; edge labeling

Abstract: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.