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Harmonious chromatic number of directed graphs

✍ 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

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On the harmonious chromatic number of a
✍ John Mitchem πŸ“‚ Article πŸ“… 1989 πŸ› Elsevier Science 🌐 English βš– 755 KB

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

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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. 345–347 and 629–636) and the lower bound given by D. G. Beane, N. L. Biggs, and B. J. Wilson (__Journal of Graph T

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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