If the vertices of a graph G are partitioned into k classes V~, I/2 ..... Vk such that each V~ is an independent set and I1V~I-IV~[I ~< 1 for all i#j, then G is said to be equitably colored with k colors. The smallest integer n for which G can be equitably colored with n colors is called the equitab
On the harmonious coloring of collections of graphs
β Scribed by John P. Georges
- Publisher
- John Wiley and Sons
- Year
- 1995
- Tongue
- English
- Weight
- 741 KB
- Volume
- 20
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
The hermonious coloring number of the graph G, HC(G), is the smallest number of colors needed to label the vertices of G such that adjacent vertices received different colors and no two edges are incident with the same color pair. In this paper, we investigate the HCβnumber of collections of disjoint paths, cycles, complete graphs, and complete bipartite graphs. We determine exact expressions for the HCβnumber of collections of paths and 4__m__βcycles. Β© 1995, John Wiley & Sons, Inc.
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