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    Please use this identifier to cite or link to this item: https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/121001

    Title: Shifted-Antimagic Labelings for Graphs
    Authors: Chang, Fei-Huang;Chen, Hong-Bin;Li, Wei-Tian;Pan, Zhishi
    Keywords: Antimagic labeling;Disconnected graphs;Trees
    Date: 2021-03-30
    Issue Date: 2021-08-24 12:11:23 (UTC+8)
    Publisher: Springer Nature
    Abstract: 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.
    Relation: Graphs and Combinatorics,37,p.1065–1082
    DOI: 10.1007/s00373-021-02305-w
    Appears in Collections:[Graduate Institute & Department of Mathematics] Journal Article

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