Pair labelings of graphs

Given a graph $G$ and positive integer $d$, the pair-labeling number $r^* (G,d)$ is the minimum $n$ such that each vertex in $G$ can be assigned a pair of numbers from $\{ 0,1, \cdots ,n - 1 \}$ so that any two numbers used at adjacent vertices differ by at least $d$ modulo $n$. All possible values...

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Bibliographic Details
Published inSIAM journal on discrete mathematics Vol. 5; no. 1; pp. 144 - 149
Main Authors GUICHARD, D. R, KRUSSEL, J. W
Format Journal Article
LanguageEnglish
Published Philadelphia, PA Society for Industrial and Applied Mathematics 01.02.1992
Subjects
Applied mathematics
Combinatorics
Combinatorics. Ordered structures
Exact sciences and technology
Graph theory
Graphs
Labeling
Mathematics
Sciences and techniques of general use
Connected graph
Graph labelling
Chromatic number
Extremum problem
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Summary:Given a graph $G$ and positive integer $d$, the pair-labeling number $r^* (G,d)$ is the minimum $n$ such that each vertex in $G$ can be assigned a pair of numbers from $\{ 0,1, \cdots ,n - 1 \}$ so that any two numbers used at adjacent vertices differ by at least $d$ modulo $n$. All possible values of $r^* (G,d)$, given the chromatic number of $G$, are determined.
ISSN:0895-4801
1095-7146
DOI:10.1137/0405012