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    题名: Shifted-Antimagic Labelings for Graphs
    作者: Chang, Fei-Huang;Chen, Hong-Bin;Li, Wei-Tian;Pan, Zhishi
    关键词: Antimagic labeling;Disconnected graphs;Trees
    日期: 2021-03-30
    上传时间: 2021-04-08 12:10:19 (UTC+8)
    摘要: The concept of antimagic labelings of a graph is to produce distinct vertex sums by labeling edges through consecutive numbers starting from one. A long-standing conjecture is that every connected graph, except a single edge, is antimagic. Some graphs are known to be antimagic, but little has been known about sparse graphs, not even trees. This paper studies a weak version called k-shifted-antimagic labelings which allow the consecutive numbers starting from k+1, instead of starting from 1, where k can be any integer. This paper establishes connections among various concepts proposed in the literature of antimagic labelings and extends previous results in three aspects:
    -Some classes of graphs, including trees and graphs whose vertices are of odd degrees, which have not been verified to be antimagic are shown to be k-shifted-antimagic for sufficiently large k.
    -Some graphs are proved k-shifted-antimagic for all k, while some are proved not for some particular k.
    -Disconnected graphs are also considered.
    關聯: Graphs and Combinatorics 37(2)
    DOI: 10.1007/s00373-021-02305-w
    显示于类别:[會計學系暨研究所] 期刊論文


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