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Indexed by:期刊论文

Date of Publication:2009-01-01

Journal:ARS COMBINATORIA

Included Journals:SCIE、Scopus

Volume:90

Page Number:411-421

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, for some positive integers a and d, if its edges admit a labeling by all the integers in the set {1, 2, ..., vertical bar E(G)vertical bar} such that the induced vertex labels, obtained by adding all the labels of the edges adjacent to each vertex, consist of an arithmetic progression with the first term a and the common difference d. Mirka Miller and Mai-tin Bac-a proved that, the generalized Petersen graph P(n, 2) is (3n+6/2, 3)-aritiniagic for n = 0 (mod 4), n >= 8 and conjectured that P(n, k) is (3n+6/2, 3) antimagic for even n and 2 <= k <= n/2. The first author of this 2 paper proved that P(n, 3) is (3n+6/2, 3)-antimagic for even n >= 6. In 2 this paper, we show that the generalized Petersen graph P(n, 2) is 3)-aritimagic for n equivalent to 2 (mod 4), n >= 10.