Radio Graceful Hamming Graphs

Amanda 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 -