The harmonious chromatic number of a graph G, denoted by h(G), is the least number of colon which can be assigned to the vertices of G such that adjacent vertices are colored differently and any two distinct edges have different color pairs. This is a slight variation of a definition given independe
Harmonious chromatic number of directed graphs
β Scribed by Keith J. Edwards
- Book ID
- 119225073
- Publisher
- Elsevier Science
- Year
- 2013
- Tongue
- English
- Weight
- 225 KB
- Volume
- 161
- Category
- Article
- ISSN
- 0166-218X
No coin nor oath required. For personal study only.
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## Abstract The upper bound for the harmonious chromatic number of a graph given by Zhikang Lu and by C. McDiarmid and Luo Xinhua, independently (__Journal of Graph Theory__, 1991, pp. 345β347 and 629β636) and the lower bound given by D. G. Beane, N. L. Biggs, and B. J. Wilson (__Journal of Graph T
An upper bound for the harmonious chromatic number of a graph G is given. Three corollaries of the theorem are theorems or improvements of the theorems of Miller and Pritikin. The assignment of colors to the vertices of a graph such that each vertex has exactly one color has been studied for well o