Abstract
A labeling f of a graph G is a bijection from its edge set E(G) to the set {1,2,..., |E(G)|}, which is antimagic if for any distinct vertices x and y, the sum of the labels on edges incident to x is different from the sum of the labels on edges incident to y. A graph G is antimagic if G has an f which is antimagic. Hartsfield and Ringel conjectured in 1990 that every connected graph other than K 2 is antimagic. In this paper, we show that if G 1 is an m-vertex graph with maximum degree at most 6r+1, and G 2 is an n-vertex (2r)-regular graph (m⩾n⩾3), then the join graph G 1 ∨ G 2 is antimagic.
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Foundation item: Supported by the National Natural Science Foundation of China(11371052,11271267,10971144,11101020), the Natural Science Foundation of Beijing (1102015), the Fundamental Research Funds for the Central Universities(2011B019, 3142013104)
Biography: WANG Tao, male, Master, Associate professor, research direction: graph theory.
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Wang, T., Li, D. A new class of antimagic join graphs. Wuhan Univ. J. Nat. Sci. 19, 153–155 (2014). https://doi.org/10.1007/s11859-014-0993-5
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DOI: https://doi.org/10.1007/s11859-014-0993-5