# Radio Graceful Hamming Graphs

Discussiones Mathematicae Graph Theory (2016)

- Volume: 36, Issue: 4, page 1007-1020
- ISSN: 2083-5892

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topAmanda Niedzialomski. "Radio Graceful Hamming Graphs." Discussiones Mathematicae Graph Theory 36.4 (2016): 1007-1020. <http://eudml.org/doc/287074>.

@article{AmandaNiedzialomski2016,

abstract = {For k ∈ ℤ+ and G a simple, connected graph, a k-radio labeling f : V (G) → ℤ+ of G requires all pairs of distinct vertices u and v to satisfy |f(u) − f(v)| ≥ k + 1 − d(u, v). We consider k-radio labelings of G when k = diam(G). In this setting, f is injective; if f is also surjective onto \{1, 2, . . . , |V (G)|\}, then f is a consecutive radio labeling. Graphs that can be labeled with such a labeling are called radio graceful. In this paper, we give two results on the existence of radio graceful Hamming graphs. The main result shows that the Cartesian product of t copies of a complete graph is radio graceful for certain t. Graphs of this form provide infinitely many examples of radio graceful graphs of arbitrary diameter. We also show that these graphs are not radio graceful for large t.},

author = {Amanda Niedzialomski},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {radio labeling; radio graceful graph; Hamming graph},

language = {eng},

number = {4},

pages = {1007-1020},

title = {Radio Graceful Hamming Graphs},

url = {http://eudml.org/doc/287074},

volume = {36},

year = {2016},

}

TY - JOUR

AU - Amanda Niedzialomski

TI - Radio Graceful Hamming Graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2016

VL - 36

IS - 4

SP - 1007

EP - 1020

AB - For k ∈ ℤ+ and G a simple, connected graph, a k-radio labeling f : V (G) → ℤ+ of G requires all pairs of distinct vertices u and v to satisfy |f(u) − f(v)| ≥ k + 1 − d(u, v). We consider k-radio labelings of G when k = diam(G). In this setting, f is injective; if f is also surjective onto {1, 2, . . . , |V (G)|}, then f is a consecutive radio labeling. Graphs that can be labeled with such a labeling are called radio graceful. In this paper, we give two results on the existence of radio graceful Hamming graphs. The main result shows that the Cartesian product of t copies of a complete graph is radio graceful for certain t. Graphs of this form provide infinitely many examples of radio graceful graphs of arbitrary diameter. We also show that these graphs are not radio graceful for large t.

LA - eng

KW - radio labeling; radio graceful graph; Hamming graph

UR - http://eudml.org/doc/287074

ER -

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