Wszystkie pola: Radio labeling - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Radio numbers for generalized prism graphs
Autorzy:: Martinez, Paul
Ortiz, Juan
Tomova, Maggy
Wyels, Cindy
Powiązania:: https://bibliotekanauki.pl/articles/744118.pdf
Data publikacji:: 2011
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: radio number
radio labeling
prism graphs
Opis:: A radio labeling is an assignment c:V(G) → N such that every distinct pair of vertices u,v satisfies the inequality d(u,v) + |c(u)-c(v)| ≥ diam(G) + 1. The span of a radio labeling is the maximum value. The radio number of G, rn(G), is the minimum span over all radio labelings of G. Generalized prism graphs, denoted $Z_{n,s}$, s ≥ 1, n ≥ s, have vertex set {(i,j) | i = 1,2 and j = 1,...,n} and edge set {((i,j),(i,j ±1))} ∪ {((1,i),(2,i+σ)) | σ = -⌊(s-1)/2⌋...,0,...,⌊s/2⌋}. In this paper we determine the radio number of $Z_{n,s}$ for s = 1,2 and 3. In the process we develop techniques that are likely to be of use in determining radio numbers of other families of graphs.
Źródło:: Discussiones Mathematicae Graph Theory; 2011, 31, 1; 45-62
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Radio Graceful Hamming Graphs
Autorzy:: Niedzialomski, Amanda
Powiązania:: https://bibliotekanauki.pl/articles/31340550.pdf
Data publikacji:: 2016-11-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: radio labeling
radio graceful graph
Hamming graph
Opis:: For $ k \in \mathbb{Z}_+ $ and $G$ a simple, connected graph, a $k$-radio labeling $ f : V (G) \rightarrow \mathbb{Z}_+ $ of $G$ requires all pairs of distinct vertices $u$ and $v$ to satisfy $ |f(u) − f(v)| \ge k + 1 − d(u, v) $. We consider $k$-radio labelings of $G$ when $ k = \text{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 $t$.
Źródło:: Discussiones Mathematicae Graph Theory; 2016, 36, 4; 1007-1020
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

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