Radio Graceful Hamming Graphs

• Autorzy: Amanda Niedzialomski
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

radio labeling; radio graceful graph; Hamming graph

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2016
• Tom: 36
• Numer: 4
• Strony: 1007-1020

Daty

wydano

2016-11-01

otrzymano

2015-07-31

poprawiono

2016-01-16

zaakceptowano

2016-01-16

online

2016-10-21

Twórcy

autor

Amanda Niedzialomski

• University of Tennessee at Martin,

Identyfikatory

DOI

10.7151/dmgt.1910