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2011 Vertex-coloring Edge-weightings of Graphs
Gerard J. Chang, Changhong Lu, Jiaojiao Wu, Qinglin Yu
Taiwanese J. Math. 15(4): 1807-1813 (2011). DOI: 10.11650/twjm/1500406380

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 $r \ge 3$.

Citation

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Gerard J. Chang. Changhong Lu. Jiaojiao Wu. Qinglin Yu. "Vertex-coloring Edge-weightings of Graphs." Taiwanese J. Math. 15 (4) 1807 - 1813, 2011. https://doi.org/10.11650/twjm/1500406380

Information

Published: 2011
First available in Project Euclid: 18 July 2017

zbMATH: 1235.05048
MathSciNet: MR2848990
Digital Object Identifier: 10.11650/twjm/1500406380

Subjects:
Primary: 05C15

Rights: Copyright © 2011 The Mathematical Society of the Republic of China

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