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 OJDM  Vol.11 No.3 , July 2021
A Note on n-Set Distance-Labelings of Graphs
Abstract: This note is considered as a sequel of Yeh [1]. Here, we present a generalized (vertex) distance labeling (labeling vertices under constraints depending the on distance between vertices) of a graph. Instead of assigning a number (label) to each vertex, we assign a set of numbers to each vertex under given conditions. Some basic results are given in the first part of the note. Then we study a particular class of this type of labelings on several classes of graphs.
Cite this paper: Yeh, R. (2021) A Note on n-Set Distance-Labelings of Graphs. Open Journal of Discrete Mathematics, 11, 55-60. doi: 10.4236/ojdm.2021.113005.
References

[1]   Yeh, R.K. (2019) Pair L(2,1)-Labelings of Infinite Graphs. Discussiones Mathematicae Graph Theory, 39, 257-269.
https://doi.org/10.7151/dmgt.2077

[2]   Roberts, F.S. (1988) Private Communication with Griggs J. R.

[3]   Griggs, J.R. and Yeh, R.K. (1992) Labelling Graphs with a Condition at Distance 2. SIAM Journal on Discrete Mathematics, 5, 586-595.
https://doi.org/10.1137/0405048

[4]   Calamoneri, T. (2011) The L(h,k)-Labeling Problems: A Update Survey and Annotated Bibliography. The Computer Journal, 54, 1344-1371.
https://doi.org/10.1093/comjnl/bxr037

[5]   Yeh, R.K. (2006) A Survey on Labeling Graphs with a Condition at Distance Two. Discrete Mathematics, 306, 1217-1231.
https://doi.org/10.1016/j.disc.2005.11.029

[6]   Füredi, Z., Griggs, J.R. and Kleitman, D.J. (1989) Pair Labellings with Given Distance. SIAM Journal on Discrete Mathematics, 2, 491-499.
https://doi.org/10.1137/0402044

[7]   Griggs, J.R. and Jin, X.T. (2008) Real Number Channel Assignments for Lattices. SIAM Journal on Discrete Mathematics, 22, 996-1021.
https://doi.org/10.1137/060650982

[8]   Liu, D.D.-F. and Yeh, R.K. (1997)On Distance Two Labelings of Graphs. Ars Combinatoria, 47, 13-22.

 
 
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