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.
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.
