Pair labelings of graphs

• Published in: SIAM journal on discrete mathematics Vol. 5; no. 1; pp. 144 - 149
• Main Authors: GUICHARD, D. R, KRUSSEL, J. W
• Format: Journal Article
• Language: English
• 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

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...