Neighborhood Coloring Number of a Graph
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For a graph G = (V,E), the δ-neighborhood coloring number Χδn(G)is the minimum number of colors used in a proper coloring of the vertices of G such that for each vertex v, v is adjacent to at least δ color classes. We initiate a study of the δ-neighborhood coloring number of a graph and obtain some bounds, besides finding the exact value of this parameter for some graphs.
Abstract
For a graph G = (V,E), the δ-neighborhood coloring number Χδn(G)is the minimum number of colors used in a proper coloring of the vertices of G such that for each vertex v, v is adjacent to at least δ color classes. We initiate a study of the δ-neighborhood coloring number of a graph and obtain some bounds, besides finding the exact value of this parameter for some graphs.
참고문헌 (5)
- C. Berge, "The theory of graphs and its applications" (1962), Methuen
- Bruce Montgomery, "Dynamic Coloring of Graphs", pp.2001
- F. Harary, "Graph Theory" (1969), Addison-Wesley Publishing Company, Inc
- Harary F., "The square of a tree", Bell syst. Tech. J, 39, pp.641~647 (1960)
- O. Ore, "Theory of Graphs", pp.38~ (1962), Amer. Math. Soc. Colloq. Publ.