Antimagic labeling of biregular bipartite graphs
Antimagic labeling of biregular bipartite graphs
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双正则二部图的 Antimagic 标记
DOI：
10.1016/j.dam.2022.11.019
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发表时间：
2022-12-14
影响因子：
1.1
通讯作者：
Yu, Xiaowei
中科院分区：
文献类型：
--
作者：
Yu, Xiaowei
n阶m边图G的反幻标号是从G的边集到{1，2，...，m}使得所有n个顶点的顶点和是两两不同的，其中一个顶点的顶点和是与它相关联的边的标号之和.我们说一个图是反魔图，如果它有一个反魔标号. 1990年，Hartsfield和Ringel证明了每个至少有三个顶点的连通图都是反魔术的，这就是所谓的反魔术标号猜想。这个猜想似乎很困难，而且到目前为止还没有被证明是树。最近，它已被证明是正确的正则二部图和正则图独立。然而，它仍然是未知的，是否每个双正则二部图是反魔术。在本文中，我们几乎肯定地回答了这个问题。(c)2022爱思唯尔有限公司版权所有。
An antimagic labeling of a graph G with n vertices and m edges is a bijection from the set of edges of G to {1, 2, ... , m} such that all n vertex-sums are pairwise distinct, where the vertex-sum of a vertex is the sum of labels on the edges incident with it. We say a graph is antimagic if it has an antimagic labeling. In 1990, Hartsfield and Ringel conjectured every connected graph with at least three vertices is antimagic, which is known as the Antimagic Labeling Conjecture. This conjecture seems difficult, and it has not been certified for trees so far. Recently, it has been verified to be true for regular bipartite graphs and regular graphs independently. However, it remained unknown whether every biregular bipartite graph is antimagic. In this paper, we almost answer this question affirmatively.(c) 2022 Elsevier B.V. All rights reserved.