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- W261688557 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 } ." @default.
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- W261688557 date "2015-10-01" @default.
- W261688557 modified "2023-10-16" @default.
- W261688557 title "Neighbor sum distinguishing edge colorings of sparse graphs" @default.
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- W261688557 doi "https://doi.org/10.1016/j.dam.2015.04.018" @default.
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