Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak harmonic labeling of graphs and multigraphs   In this article we introduce the notion of weak harmonic labeling of a graph,
a generalization of the concept of harmonic labeling defined recently by
Benjamini et al. that allows extension to finite graphs and graphs with leaves.
We present various families of examples and provide several constructions that
extend a given weak harmonic labeling to larger graphs. In particular, we use
finite weak models to produce new examples of (strong) harmonic labelings. As a
main result, we provide a characterization of weakly labeled graphs in terms of
harmonic subsets of the integers and use it to compute every such graphs of up
to ten vertices. In particular, we characterize harmonically labeled graphs as
defined by Benjamini et al. We further extend the definitions and main results
to the case of multigraphs and total labelings.

28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat