A Generalized Version of a Local Antimagic Labelling Conjecture

作者：Lyngsie, Kasper Szabo; Zhong, Liang^*

来源：Graphs and Combinatorics, 2018, 34(6): 1363-1369.

DOI：10.1007/s00373-018-1936-2

• Antimagic labelling
• Local antimagic labelling
• Neighbour sum distinguishing edge weightings

An antimagic labelling of a graph G with m edges is a bijection f : E(G) -> {1, . . . , m} such that for any two distinct vertices u, v we hav Sigma(e is an element of E(v)) f (e) not equal Sigma(e is an element of E(u)) f (e), where E(v) denotes the set of edges incident v. The well-known Antimagic Labelling Conjecture formulated in 1994 by Hartsfield and Ringel states that any connected graph different from K-2 admits an antimagic labelling. A weaker local version which we call the Local Antimagic Labelling Conjecture says that if G is a graph distinct from K-2, then there exists a bijection f : E(G) -> {1, . . . , vertical bar E(G)vertical bar} such that for any two neighbours u, v we hav Sigma(e is an element of E(v)) f (e) not equal Sigma(e is an element of E(u)) f (e). This paper proves the following more general list version of the local antimagic labelling conjecture: Let G be a connected graph with m edges which is not a star. For any list L of m distinct real numbers, there is a bijection f : E(G) -> L such that for any pair of neighbours u, v we have that Sigma(e is an element of E(v)) f (e) not equal Sigma(e is an element of E(u)) f (e).

• 出版日期2018-11
• 单位福州大学