Shifted-Antimagic Labelings for Graphs

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Title:	Shifted-Antimagic Labelings for Graphs
Authors:	Pan, Zhi-shi
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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