Taiwanese Journal of Mathematics

Vertex-coloring Edge-weightings of Graphs

Gerard J. Chang, Changhong Lu, Jiaojiao Wu, and Qinglin Yu

Full-text: Open access

Abstract

A $k$-edge-weighting of a graph $G$ is a mapping $w: E(G) \to \{1,2,\ldots, k\}$. An edge-weighting $w$ induces a vertex coloring $f_w: V(G) \to \mathbb{N}$ defined by $f_w(v) = \sum_{v \in e} w(e)$. An edge-weighting $w$ is vertex-coloring if $f_w(u) \ne f_w(v)$ for any edge $uv$. The current paper studies the parameter $\mu(G)$, which is the minimum $k$ for which $G$ has a vertex-coloring $k$-edge-weighting. Exact values of $\mu(G)$ are determined for several classes of graphs, including trees and $r$-regular bipartite graph with $r \ge 3$.

Article information

Source
Taiwanese J. Math., Volume 15, Number 4 (2011), 1807-1813.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406380

Digital Object Identifier
doi:10.11650/twjm/1500406380

Mathematical Reviews number (MathSciNet)
MR2848990

Zentralblatt MATH identifier
1235.05048

Subjects
Primary: 05C15: Coloring of graphs and hypergraphs

Keywords
edge-weighting vertex-coloring tree bipartite graph

Citation

Chang, Gerard J.; Lu, Changhong; Wu, Jiaojiao; Yu, Qinglin. Vertex-coloring Edge-weightings of Graphs. Taiwanese J. Math. 15 (2011), no. 4, 1807--1813. doi:10.11650/twjm/1500406380. https://projecteuclid.org/euclid.twjm/1500406380


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