Geodesic
Coprime and prime labelings of graphs
Journal of integer sequences, Tome 19 (2016) no. 5
A coprime labeling of a simple graph of order $n$ is a labeling in which adjacent vertices are given relatively prime labels, and a graph is prime if the labels used can be taken to be the first $n$ positive integers. In this paper, we consider when ladder graphs are prime and when the corresponding labeling may be done in a cyclic manner around the vertices of the ladder. Furthermore, we discuss coprime labelings for complete bipartite graphs.
Classification : 05C78, 11A05
Keywords: coprime labeling, prime labeling, prime graph, consecutive cyclic prime labeling, bipartite graph, ladder graph, Ramanujan prime 
@article{JIS_2016__19_5_a0,
     author = {Berliner,  Adam H. and Dean,  Nathaniel and Hook,  Jonelle and Marr,  Alison and Mbirika,  Aba and McBee,  Cayla D.},
     title = {Coprime and prime labelings of graphs},
     journal = {Journal of integer sequences},
     year = {2016},
     volume = {19},
     number = {5},
     zbl = {1342.05127},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2016__19_5_a0/}
}
TY  - JOUR
AU  - Berliner,  Adam H.
AU  - Dean,  Nathaniel
AU  - Hook,  Jonelle
AU  - Marr,  Alison
AU  - Mbirika,  Aba
AU  - McBee,  Cayla D.
TI  - Coprime and prime labelings of graphs
JO  - Journal of integer sequences
PY  - 2016
VL  - 19
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/JIS_2016__19_5_a0/
LA  - en
ID  - JIS_2016__19_5_a0
ER  - 
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%A Berliner,  Adam H.
%A Dean,  Nathaniel
%A Hook,  Jonelle
%A Marr,  Alison
%A Mbirika,  Aba
%A McBee,  Cayla D.
%T Coprime and prime labelings of graphs
%J Journal of integer sequences
%D 2016
%V 19
%N 5
%U http://geodesic.mathdoc.fr/item/JIS_2016__19_5_a0/
%G en
%F JIS_2016__19_5_a0
Berliner,  Adam H.; Dean,  Nathaniel; Hook,  Jonelle; Marr,  Alison; Mbirika,  Aba; McBee,  Cayla D. Coprime and prime labelings of graphs. Journal of integer sequences, Tome 19 (2016) no. 5. http://geodesic.mathdoc.fr/item/JIS_2016__19_5_a0/