Taiwanese Journal of Mathematics

T-COLORING ON FOLDED HYPERCUBES

Justie Su-Tzu Juan, I-fan Sun, and Pin-Xian Wu

Full-text: Open access

Abstract

Given a graph $G=(V,E)$ and a set $T$ of non-negative integers containing $0$, a $T$-coloring of $G$ is an integer function $f$ of the vertices of $G$ such that $|f(u)-f(v)| \notin T$ whenever $uv \in E$. The edge-span of a $T$-coloring $f$ is the maximum value of $|f(u)-f(v)|$ over all edges $uv$, and the $T$-edge-span of a graph $G$ is the minimum value of the edge-span among all possible $T$-colorings of $G$. This paper discusses the $T$-edge span of the folded hypercube network of dimension $n$ for the $k$-multiple-of-$s$ set, $T=\{ 0$, $s$, $2s$, $\dots$, $ks\} \cup S$, where $s$ and $k \geq 1$ and $S \subseteq \{ s+1, s+2, \dots , ks-1 \}$.

Article information

Source
Taiwanese J. Math., Volume 13, Number 4 (2009), 1331-1341.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405511

Digital Object Identifier
doi:10.11650/twjm/1500405511

Mathematical Reviews number (MathSciNet)
MR2543746

Zentralblatt MATH identifier
1201.05038

Subjects
Primary: 05C15: Coloring of graphs and hypergraphs

Keywords
$T$-coloring binary folded hypercube $T$-edge-span

Citation

Juan, Justie Su-Tzu; Sun, I-fan; Wu, Pin-Xian. T-COLORING ON FOLDED HYPERCUBES. Taiwanese J. Math. 13 (2009), no. 4, 1331--1341. doi:10.11650/twjm/1500405511. https://projecteuclid.org/euclid.twjm/1500405511


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