Back to Search
Start Over
Neighbor sum distinguishing edge colorings of sparse graphs.
- Source :
-
Discrete Applied Mathematics . Oct2015, Vol. 193, p119-125. 7p. - Publication Year :
- 2015
-
Abstract
- We consider proper edge colorings of a graph G using colors of the set { 1 , … , k } . Such a coloring is called neighbor sum distinguishing if for any u v ∈ E ( G ) , the sum of colors of the edges incident to u is different from the sum of the colors of the edges incident to v . The smallest value of k in such a coloring of G is denoted by ndi Σ ( G ) . Let mad ( G ) and Δ ( G ) denote the maximum average degree and the maximum degree of a graph G , respectively. In this paper we show that, for a graph G without isolated edges, if mad ( G ) < 8 3 , then ndi Σ ( G ) ≤ max { Δ ( G ) + 1 , 7 } ; and if mad ( G ) < 3 , then ndi Σ ( G ) ≤ max { Δ ( G ) + 2 , 7 } . [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0166218X
- Volume :
- 193
- Database :
- Academic Search Index
- Journal :
- Discrete Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 108505151
- Full Text :
- https://doi.org/10.1016/j.dam.2015.04.018