• Corpus ID: 227227739

Weak harmonic labeling of graphs and multigraphs.

@article{Bonucci2020WeakHL,
  title={Weak harmonic labeling of graphs and multigraphs.},
  author={Pablo Leandro Bonucci and N. Capitelli},
  journal={arXiv: Combinatorics},
  year={2020}
}
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… 

References

SHOWING 1-7 OF 7 REFERENCES
Harmonic labeling of graphs
A Dynamic Survey of Graph Labeling
A graph labeling is an assignment of integers to the vertices or edges, or both, subject to certain conditions. Graph labelings were first introduced in the late 1960s. In the intervening years
Applications of numbered undirected graphs
TLDR
An attempt has been made to systematically present all of these diverse applications ofumbered undirected graphs in a unifying framework and to indicate the existence of additional applications and to suggest directions for additional research.
Numbered complete graphs, unusual rulers, and assorted applications
TLDR
A survey was made of three such numberings, their relation to "ruler models," and their applications to x-ray crystallography, to codes for radar, missile guidance, and angular synchronization, to convolutional codes, to addressing in communications networks, and to an integral voltage generator.
E
  • Procaccia & R. Tessler. Harmonic labeling of graphs. Discrete Math., 313 (17), 1726-1745
  • 2013
Graphs and Geometry
Numbered complete graphs
  • unusual rulers, and assorted applications. In Theory and Applications of Graphs, Lecture Notes in Math. (642), Springer-Verlag New York, 53-65
  • 1978