Neighbor sum distinguishing total coloring of 2-degenerate graphs

@article{Yao2017NeighborSD,
  title={Neighbor sum distinguishing total coloring of 2-degenerate graphs},
  author={Jing Jing Yao and Xiaowei Yu and G. Wang and Changqing Xu},
  journal={Journal of Combinatorial Optimization},
  year={2017},
  volume={34},
  pages={64-70}
}
A proper k-total coloring of a graph G is a mapping from $$V(G)\cup E(G)$$V(G)∪E(G) to $$\{1,2,\ldots ,k\}$${1,2,…,k} such that no two adjacent or incident elements in $$V(G)\cup E(G)$$V(G)∪E(G) receive the same color. Let f(v) denote the sum of the colors on the edges incident with v and the color on vertex v. A proper k-total coloring of G is called neighbor sum distinguishing if $$f(u)\ne f(v)$$f(u)≠f(v) for each edge $$uv\in E(G)$$uv∈E(G). Let $$\chi ''_{\Sigma }(G)$$χΣ′′(G) denote the… 
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