Neighbor sum distinguishing list total coloring of subcubic graphs

Abstract

Let $$G=(V, E)$$ be a simple graph and denote the set of edges incident to a vertex v by E(v). The neighbor sum distinguishing (NSD) total choice number of G, denoted by $$\mathrm{ch}_{\Sigma }^{t}(G)$$ , is the smallest integer k such that, after assigning each $$z\in V\cup E$$ a set L(z) of k real numbers, G has a total coloring $$\phi $$ satisfying $$\phi (z)\in L(z)$$ for each $$z\in V\cup E$$ and $$\sum _{z\in E(u)\cup \{u\}}\phi (z)\ne \sum _{z\in E(v)\cup \{v\}}\phi (z)$$ for each $$uv\in E$$ . In this paper, we propose some reducible configurations of NSD list total coloring for general graphs by applying the Combinatorial Nullstellensatz. As an application, we present that $$\mathrm{ch}^{t}_{\Sigma }(G)\le \Delta (G)+3$$ for every subcubic graph G.