Introduction to dominated edge chromatic number of a graph
| Autor: | Saeid Alikhani, Mohammad R. Piri |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Vertex (graph theory)
lcsh:T57-57.97 General Mathematics dominated edge chromatic number Edge (geometry) Graph Prime (order theory) operation Combinatorics Edge coloring 05C25 Computer Science::Discrete Mathematics subdivision lcsh:Applied mathematics. Quantitative methods FOS: Mathematics Mathematics - Combinatorics Chromatic scale Combinatorics (math.CO) corona Mathematics |
| Zdroj: | Opuscula Mathematica, Vol 41, Iss 2, Pp 245-257 (2021) |
| DOI: | 10.48550/arxiv.2003.10232 |
| Popis: | We introduce and study the dominated edge coloring of a graph. A dominated edge coloring of a graph $G$ is a proper edge coloring of $G$ such that each color class is dominated by at least one edge of $G$. The minimum number of colors among all dominated edge coloring is called the dominated edge chromatic number, denoted by $\chi_{dom}^{\prime}(G)$. We obtain some properties of $\chi_{dom}^{\prime}(G)$ and compute it for specific graphs. Also we examine the effects on $\chi_{dom}^{\prime}(G)$ when $G$ is modified by operations on vertex and edge of $G$. Finally, we consider the $k$-subdivision of $G$ and study the dominated edge chromatic number of these kind of graphs. Comment: 12 pages, 12 figures. arXiv admin note: text overlap with arXiv:1801.08871 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|