Publication Date
4-1-2021
Document Type
Article
Publication Title
Iranian Journal of Mathematical Sciences and Informatics
Volume
16
Issue
1
DOI
10.29252/ijmsi.16.1.1
First Page
1
Last Page
13
Abstract
Let G = (V (G),E(G)) be a simple, finite and undirected graph of order n. A k-vertex weighting of a graph G is a mapping w: V (G) → {1,…, k}. A k-vertex weighting induces an edge labeling fw: E(G) → N such that fw(uv) = w(u) + w(v). Such a labeling is called an edge-coloring k-vertex weighting if fw(e)≠ fw(e′) for any two adjacent edges e and e′. Denote by μ′(G) the minimum k for G to admit an edge-coloring k-vertex weighting. In this paper, we determine μ′(G) for some classes of graphs.
Keywords
Edge coloring, Vertex weighting
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License
Department
Mathematics and Statistics
Recommended Citation
Wai Chee Shiua, Gee Choon Lau, and Ho Kuen Ng. "Edge-coloring vertex-weighting of graphs" Iranian Journal of Mathematical Sciences and Informatics (2021): 1-13. https://doi.org/10.29252/ijmsi.16.1.1
