Abstract

Let be a graph. A vertex coloring of is called -vertex coloring if for every vertex of , where is the set of colors of vertices adjacent to . Let be the maximum number of colors used in an -vertex coloring of . We provide some lower and upper bounds for in terms of girth, diameter or size of . Also, for every tree , we obtain .

Metadata

publication

Discrete Mathematics, Algorithms and Applications 10 (01), 1850007, 2018

year

2018

publication date

2018/2/30

authors

S Akbari, Nazanin Alipourfard, P Jandaghi, M Mirtaheri

link

https://www.worldscientific.com/doi/abs/10.1142/S1793830918500076

journal

Discrete Mathematics, Algorithms and Applications

volume

10

issue

01

pages

1850007

publisher

World Scientific Publishing Company