Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Shifted-antimagic Labelings for Graphs   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:
  $\bullet$ 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 $k$.
  $\bullet$ Some graphs are proved $k$-shifted-antimagic for all $k$, while
some are proved not for some particular $k$.
  $\bullet$ Disconnected graphs are also considered.

12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org