Neighbor sum distinguishing total chromatic number of 2-degenerate graphs

Abstract Let G = ( V ( G ) , E ( G ) ) be a graph and ϕ be a proper total k -coloring of G by using the color set { 1 , 2 , … , k } . For any v ∈ V ( G ) , let f ( v ) = ∑ u v ∈ E ( G ) ϕ ( u v ) + ϕ ( v ) . The coloring ϕ is neighbor sum distinguishing, if f ( u ) ≠ f ( v ) for each edge u v ∈ E ( G ) . The neighbor sum distinguishing total chromatic number of G , denoted by χ Σ ′ ′ ( G ) , is the smallest integer k such that G admits a k -neighbor sum distinguishing total coloring. In this paper, by using the famous Combinatorial Nullstellensatz, we determine χ Σ ′ ′ ( G ) for any 2-degenerate graph G with Δ ( G ) ≥ 6 .